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Variation  in  Pitch  Discrimination 
Within  the  Tonal  Range 


THOMAS  FRANKLIN  VaNCE 


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Reprinted  from  Psychological  Review  MonoRrap 


Variation  in  Pitch  Discrimination 
Within  the  Tonal  Range 


r.y 
THOMAS  FRANKLIN  VaNCE 


Reprinted  from   Psychological  Review  Monof^raph  No.   69 


Variation  in  Pitch  Discrimination 
Within  the  Tonal  Range 


THOMAS  FRANKLIN  VANCE 


A  thesis  submitted  to  the  Department  of  Philosophy  and  Psy- 
chology of  the  Graduate  College  in  the  State  University  of 
Iowa,  in  partial  fulfillment  of  the  Requirement  for  the  degree 
of  Doctor  of  Philosophy. 


a^3g  I 


BERK!EL£Y 

fv; USiC  L:::nAnY 
UNivnf^oiTY  or 

CALIFORNIA 


V3 


VARIATION  IN  PITCH  DISCRIMINATION  WITHIN  THE 
TONAL  RANGE 

BY 
THOMAS    FRANKLIN    VANCE 

TABLE  OF  CONTENTS 
I.  Historical  statement 
II.  Statement  of  the  problem 

1.  Apparatus 

2.  Method  and  procedure 

3.  Observers 

III.  Results 

1.  The  composite  curve 

2.  The  comparative  curve 

3.  Individual  diflferences 

4.  Relation  of  musical  training  and  expression  to  pitch  discrimmation 

5.  The  frequency  and  distribution  of  false  judgments 

6.  Differences  of  sex 

IV.  Summary 
V.  Bibliography 

HISTORICAL  STATEMENT 

The  object  in  this  brief  historical  survey  is  to  place  before  the 
reader  only  those  results  v^hich  are  most  closely  related  to  the 
present  problem  with  respect  to  the  methods  used  and  the  aspects 
investigated.  Therefore,  investigations  made  with  similar  methods 
but  having  only  a  narrow  field,  as  well  as  those  exploring  a  large 
range  by  dififerent  means,  will  not  be  discussed. 

Preyer  may  be  considered  the  pioneer  worker  on  the  problem 
of  pitch  discrimination  within  the  tonal  range.  Earlies  investigators 
concerned  themselves  with  the  least  perceptible  difference  at  only  a 
single  point  in  the  register,  Delazenne,  (i)  in  1827,  used  a  metal 
string  1 147  mm.  in  length  with  a  vibration  rate  of  60  v.d.,  which  he 
divided  into  equal  parts  by  a  bridge.  He  found  that  if  the  bridge 
was  removed  only  i  mm.  from  the  central  position  a  difference  of 
pitch  could  be  detected  by  well  trained  ears  when  the  two  parts  of 
the  string  were  sounded  in  succession.  Weber  (20)  declared  that 
he  was  able  to  determine  the  pitch  of  tones  so  accurately  through 
the  ear  that  he  never  made  an  error  of  more  than  one  vibration  on  a 
tone  of  200  v.d.    He  thought  it  possible  that  this  keen  discrimination 


^^^41.82 


ii6  '    'THOMAS  F.   VANCE 

might  be  due  to  beats.  Sauveur  (9)  with  two  monochords  tuned  to 
the  same  pitch  found  that  when  one  string  was  shortened  by  1/2000 
of  its  length  a  difference  in  the  pitch  of  the  two  tones  was  recogni- 
zable, but  he  leaves  no  record  as  to  the  pitch  of  the  tones.  Schleiber 
(12)  recorded  a  differential  threshold  of  less  than  .5  v.d.  on  the 
tone  of  b.  Seebeck  (14)  and  two  superior  violin  players  differen- 
tiated without  fail  between  two  tuning  forks  vibrating  at  1209  and 
1210  v.d. 

Preyer. — Preyer  (7)  used  the  Appunn  tonmesser, — an  instru- 
ment consisting  of  reeds  which  gave  the  following  tones :  from  500  to 
501  in  steps  differing  by  o.i  v.d.,  504,  508,  512,  1000  to  looi  in 
steps  of  0.2  v.d.,  1008,  1016,  1024,  2048,  and  4096  v.d.,  respectively. 
More  than  a  thousand  judgments  as  to  whether  the  two  tones 
compared  were  equal  or  different,  were  secured  from  twelve  prac- 
ticed observers.  They  were  not  required  to  tell  the  direction  of  the 
difference.  To  his  own  results  he  added  those  of  Delezenne  and 
Seebeck.  Transcribing  Delezenne's  measurement  in  millimeters 
into  terms  of  frequency  of  vibration,  he  found  that  the  shorter 
string  produced  a  tone  of  120.2  v.d.,  while  the  longer  one  gave  a 
tone  of  1 19.8  v.d.,  thus  making  a  difference  of  0.4  v.d.  which  skilled 
observers  could  detect.  Likewise,  a  simple  computation  revealed  the 
fact  that  Seebeck  had  the  very  low  threshold  of  0.36  at  449  v.d. 
After  some  verification  of  Seebeck's  results,  Preyer  inclined  to  the 
belief  that  the  threshold  might  be  brought  as  low  as  0.25  v.d.  The 
combined  results  give  differential  thresholds  for  four  different  places 
in  the  tonal  range  as  follows:  Delezenne  at  120  v.d.  found  the 
threshold  to  be  0.4  v.d.,  Seebeck  at  440  v.d.  found  it  to  be  0.4  v.d., 
Preyer  at  500  v.d.,  0.3  v.d.,  and  at  looo  v.d.,  0.2  v.d.  From  this 
study,  inadequate  as  it  may  seem,  Preyer  draws  the  following 
conclusions : 

(i)  One-third  of  a  vibration  on  500  v.d.  and  five-tenths  of  a 
vibration  on  1000  v.d.  will  always  be  recognized  as  different  by  the 
best  observers,  although  the  most  sensitive,  the  most  trained,  and 
the  most  reliable  ears  tested  could  not  recognize  a  difference  of  1000 
and  1000.25  v.d.  nor  of  500  and  500.2  v.d.  (2)  Very  high  tones  and 
very  low  tones  cannot  be  discriminated  so  accurately  as  tones  of 
the  middle  region.  Capacity  for  discrimination  is  keen  between  c 
and  c\  keenest  for  the  region  from  a^  to  c",  but  beyond  c^  it  de- 
creases slowly  until  it  becomes  very  unreliable  at  c^.  Fis*  marks  a 
second  point  of  keenness  of  capacity.  (3)  The  relative  difference 
for  pitch  is  dependent,  in  a  high  degree,  on  the  number  of  vibrations 


VARIATION  IM  PITCH  DISCRIMINATION  117 

of  the  compared  tones ;  and  the  absolute  (Hffercnce-sensitiveness  does 
not  decrease  with  the  pitch.  (4)  The  judgment  concerning  the  place 
of  tones  in  the  tonal  line  is  more  uncertain  than  the  judgment  as  to 
whether  the  two  tones  lie  at  different  points.  (5)  Practice  is  an 
influential  factor  in  pitch-discrimination.  Extreme  fineness  of  ca- 
pacity is  peculiar  only  to  those  who  have  much  familiarity  with 
tones. 

Luft. — In  the  Leipsic  laboratory,  during  the  years  1884  to  1886, 
Luft  (4)  experimented  upon  a  range  of  tones  extending  from  64 
to  2048  v.d.  Tuning  forks  were  used  for  the  production  of  the 
tones,  the  variable  being  mistuned  from  the  standard  by  means  of 
sliding  weights.  The  forks  64,  128,  and  256  v.d.  were  energized  by 
the  stroke  of  a  hammer  of  India-rubber,  forks  of  512  v.d.,  by  means 
of  a  violin-bow,  and  forks  of  1024  and  2048  v.d.,  by  a  wooden  ham- 
mer, which  was  padded  with  felt.  Forks  of  64  v.d.  were  held  upon 
large  resonator-boxes;  128,  256,  and  512  v.d.  were  brought  to  the 
openings  of  resonator-tubes  of  paper ;  while  1024  and  2048  v.d.  were 
permanently  attached  to  resonator-boxes.  He  used  the  method  of 
minimal  change  and  employed  from  four  to  eight  different  steps  in 
passing  from  a  large  difference  to  one  that  was  just  perceptible,  with 
the  following  results : 


Standard  v.d. 

64 

128 

256 

512 

1024 

2048 

Difference 

•IS 

.16 

.23 

.25 

.22 

.36 

"In  the  field  of  tonal  quality  within  the  region  investigated  the 
psychophysical  law,  according  to  which  the  absolute  differences  of 
sensation  correspond  to  relative  differences  of  stimulus  which  must 
be  constant,  finds  no  application.  On  the  contrary  the  differential 
threshold  within  the  interval  mentioned  approaches  the  constant 
average  of  0.2  vibrations." 

The  threshold  value  slowly  rises  from  64  to  2048  v.d.  with  the 
single  exception  of  1024  v.d.  Luft  admits  that  the  error  here  is 
probably  due  to  an  objective  circumstance.  His  results  can  scarcely 
be  compared  with  those  of  Preyer  as  the  methods  employed  were 
quite  different.  It  is  a  point  worthy  of  observation,  however,  that 
with  Preyer  the  point  of  finest  discrimination  lies  at  500  v.d.  while 
with  Luft  it  lies  at  64  v.d.  Later,  Luft  found  the  threshold  of 
32  v.d.  (by  the  same  method  employed  with  64  v.d.)  to  be  about 
.44  v.d.  His  results,  therefore,  do  not  contradict  Preyer's  statement 
that  very  high  tones  and  very  low  tones  cannot  be  distinguished  as 
readily  as  tones  of  the  middle  register. 

Luft  noted  that  practice  lowers  the  threshold  and  that  the  effect 


ii8  THOMAS  F.   VANCE 

of  practice  is  not  equally  distributed  in  all  parts  of  the  range.  The 
influence  of  practice  is  of  special  importance  at  64  and  128  v.d. 
Luft  lowered  his  own  record  from  0.85  to  0.3  v.d.  at  128  v.d.,  and 
from  0.42  to  0.15  v.d.  at  64  v.d.  He  believes  that  the  only  reason 
that  the  initial  thresholds  for  the  lower  tones  is  higher  than  those  of 
the  central  region,  is,  that  the  degree  of  practice  for  the  former  is 
not  so  great.  The  variable  of  practice  was  far  less  noticeable  in  the 
higher  regions  which  was  due,  he  believed,  to  the  greater  intensity 
and  persistence  of  these  tones.  He  even  ventured  to  say  that  the 
individual  variations  of  the  differential  threshold  are,  for  the  most 
part,  due  to  practice. 

M ever. —In  1898,  Meyer  (5)  published  Professor  Stumpf's 
thresholds  for  the  discrimination  of  pitch.  Tuning  forks  were  used 
for  the  tones  100,  200,  400,  600,  and  1200  v.d.  The  variable  forks 
were  mistuned  by  the  insertion  of  a  screw  in  the  end  of  the  prong, — 
a  more  accurate  device  than  that  of  sliding  weights.  After  discard- 
ing the  method  of  minimal  change  as  practically  worthless  for  the 
problem  in  hand,  and  thereby  questioning  the  validity  of  Luffs  re- 
sults, Meyer  adopted  the  method  of  right  and  wrong  cases.  Forks 
of  100  and  200  v.d.  were  held  in  the  hand  and  brought  to  the  open- 
ings of  the  resonators,  while  forks  of  400,  600,  and  1200  v.d.  were 
mounted  on  resonator-boxes  and  were  energized  by  the  blow  of  a 
hammer.  Each  individual  experiment  was  performed  three  times 
and  even  more  if  the  observer  wished  it,  before  a  judgment  was 
required.  In  this  manner  Meyer  thought  to  equalize  variations  of 
intensity  and  time-interval,  as  well  as  fluctuations  of  attention. 
Stumpf's  thresholds  as  determined  by  means  of  the  Cattell-Fullerton 
table,  from  the  data  given,  are  as  follows : 

V.  D 100      200      400      600     1200 

Differential     threshold         .54        -^5        -'8        -24        .69 

The  author  concluded  his  report  thus : 

"One  sees,  therefrom,  that  approximately  the  same  difference  of 
pitch  is  recognized  with  equal  certainty  at  200,  400,  and  600  v.d. 
and  with  less,  but  likewise  moderately  equal  certainty,  at  100  and 
1200  v.d.  The  differences  in  these  cases  are  so  small  that  they  may 
be  considered  accidental.  That  the  certainty  of  judgments  declines 
in  still  higher  and  still  lower  tones  is  self-evident." 

Stacker. — Stiicker's  work  (16)  is  the  most  extensive  study  pub- 
lished on  this  particular  subject.  His  observations  covered  the  range 
between  the  limits  72  and  35000  v.d.,  or  nine  entire  octaves.     He 


VARIATION  IN  PITCH  DISCRIMINATION  119 

employed  the  following  standard  tones:  d-^  (734),  c*'  (i30-5),  c^ 
(261),  all  the  tones  of  the  major  scale  up  to  c-  (522),  a-  (870), 
a^»  S^  (3^00),  c',  g\  c",  g",  c^  and  c*.  All  of  the  tones  up  to  and 
including  c-  were  produced  with  tuning  forks,  a^  and  a^  with  a 
monochord,  and  the  remaining  ones  with  a  Galton  whistle.  In  each 
individual  series  he  started  with  a  large  difference  in  the  number  of 
vibrations  of  the  two  instruments  and  then  made  the  difference 
gradually  smaller  until  the  threshold  was  reached.  Such  a  pro- 
cedure was  repeated  a  few  times  for  the  purpose  of  verification. 
Whether  the  observer  indicated  the  direction  of  the  difference  or 
merely  the  difference  is  not  stated.  Given  below  are  the  average 
values  of  the  relative  and  absolute  sensitiveness  of  discrimination 
of  his  fifty  observers  for  eight  different  levels,  with  his  statement  in 
summary : 

Pitch  d'  c"  c'  a'         a'  a'  g'  g° 

Rel.  Disc.  .94        .74        -49        -32        .30        -44        -86      4.91 

Abs.     "  .7         I.  1.3        1.4        2.5        7.7      26.7    304 

(i)  Neither  the  absolute  nor  the  relative  sensitiveness  to  difference 
of  the  two  tones  remains  constant  in  the  different  tonal  regions. 

(2)  The  relative  difference-sensitiveness  is  in  general  the  greatest  in 
the  first  and  second  accented  octaves;  in  many  cases,  however,  the 
second   maximum  lies  in  the  third  and  fourth  accented  octaves. 

(3)  With  one-third  of  the  entire  number  of  observers  the  relative 
sensitiveness  to  difference  in  the  second  half  of  the  first  accented 
octave  is  nearly  equal ;  namely,  0.2  and  0.3 ;  when  one  compares  the 
individual  curves  of  sensitiveness  with  these,  the  places  of  greatest 
sensitiveness  lie  in  the  upper  half  of  this  region,  while  with  unmusi- 
cal individuals  they  occur  in  general  in  the  lower  half.  (4)  The 
degree  of  sensitiveness  is  subjected  to  fluctuations  within  an  octave, 
which  is  repeated  in  each  octave  in  the  same  proportion ;  it  is  the 
greatest  for  c,  slightly  less  great  for  g  and  still  less  for  f  and  h. 
(5)  A  number  of  persons  possess  a  secondary  maximum  of  sensitiv- 
ity. (6)  An  unusually  great  sensitiveness  in  high  tonal  regions  is  a 
characteristic  of  musical  persons. 

Stiicker  points  out  that  the  discrimination  was  far  more  accurate 
in  the  lower  regions  when  the  second  tone  was  lower,  while  in  the 
higher  region  the  opposite  was  true.  The  inference  here  is,  that 
judgments  are  facilitated  when  the  second  tone  is  farther  removed 
from  the  first  and  second  accented  octaves,  which  are  most  fre- 
quently employed  in  musical  composition ;  i.e.,  when  the  second  tone 
is  the  farther  from  this  middle  register,  the  judgment  seems  to 
be  more  accurate.  He  further  adds,  that  the  daily  variation  of  non- 
musical  observers  is  less  than  for  musical  ones. 


120  THOMAS  F.  VANCE 

A  year  later  this  same  author  (17)  published  a  report  supple- 
menting the  one  just  reviewed.  In  this  he  states  the  results  obtained 
from  three  different  types  of  observers,  professional  players  of  varia- 
ous  instruments,  singers,  and  individuals  decidedly  unmusical.  The 
average  values  of  the  absolute  differences  for  the  three  different 
sets  of  observers  have  been  computed  for  seven  levels  in  the  tonal 
range,  as  follows : 


d' 

c" 

c^ 

a^ 

a* 

a' 

g 

Players 

.35 

•37 

.40 

.56 

1.20 

2.64 

I3-0 

Singers 

.46 

.48 

•44 

•71 

1.62 

3-07 

14.0 

Unmusical 

12.62 

2.20 

2.80 

4.80 

9.96 

24.00 

130.0 

Of  special  interest  in  this  second  article  is  the  statement  that  with 
tenors  and  sopranos  the  finest  discrimination  is  found  beneath  their 
voice  register,  but  with  bass  and  alto  singers  above  their  voice  regis- 
ter ;  the  difference  is  not  between  the  voices  of  men  and  women,  but 
only  appears  between  the  relative  height  and  depth  of  the  voice- 
register  of  both  sexes. 

The  age  difference,  he  maintains,  is  more  significant  than  that  be- 
tween musical  and  non-musical  observers.  After  the  age  of  thirty, 
sensitiveness  to  difference  declines  and  the  range  becomes  restricted. 

Schaefer. — In  1910,  Schaefer  (10)  submitted  a  thesis  to  the  De- 
partment of  Psychology  of  the  State  University  of  Iowa  on  the 
subject,  'The  Curve  for  the  Variation  of  Pitch  Discrimination 
within  the  Tonal  Range",  which  has  not  been  published.  The  ap- 
paratus and  method  were  practically  the  same  as  those  used  in  the 
present  investigation.  For  observers,  he  had  fifteen  normal  individ- 
uals varying  in  musical  ability  and  training.  Five  hundred  tests 
were  given  on  each  of  the  tones  24,  32,  64,  128,  256,  512,  and 
2048  v.d.  The  average  threshold  for  each  of  these  in  the  order 
given  is  as  follows:  3.3,  3.4,  2.9,  1.3,  1.5,  1.8,  and  6.y  v.d.  He 
summarizes  his  results  thus : 

(i)  The  form  of  the  composite  curve  indicates  that  discrimina- 
tion for  the  average  normal  individual  is  most  difficult  in  the  higher 
and  the  lower  registers  and  becomes  easier  in  the  middle  register. 
(2)  The  majority  of  the  individual  curves  are  of  the  same  form  as 
the  composite.  Curves  of  individuals  having  high  thresholds  are  of 
about  the  same  form  as  the  curves  of  individuals  having  low  thres- 
holds. (3)  There  are  notable  individual  differences.  (4)  Musical 
training  does  not  influence  to  any  large  extent,  the  ability  to  perceive 
difference  of  pitch.  (5)  It  is  easier  to  detect  difference  in  pitch  than 
to  name  the  direction  of  the  difference. 


VARIATION  IN  PITCH  DISCRIMINATION  121 

STATEMENT  OF  THE  PROBLEM 
The  primary  purpose  of  this  investigation  has  been  to  determine 
the  prevalence  of  islands  or  gaps  in  pitch-discrimination  within 
the  tonal  range.  The  pursuit  of  this  aim  has  taken  the  form  of  an 
attempt  to  make  a  comparatively  large  number  of  complete  indi- 
vidual measurements  on  pitch-discrimination  within  the  tonal  range 
with  as  many  as  possible  of  the  hitherto  unknown  or  disregarded 
sources  of  error  under  control.  On  the  basis  of  frequently  observed 
defects  in  the  hearing  of  pitch,  found  in  clinical  cases,  it  is  generally 
believed  that  such  disturbances  occur  in  varying  degrees  in  normal 
persons.  In  the  curves  of  two  or  three  of  Schaefer's  observers, 
there  are  places  where  discrimination  of  pitch  is  less  keen  than  the 
balance  of  the  curves  would  seem  to  indicate  that  it  ought  to  be ; 
in  the  case  of  one  observer  the  evidence  of  a  gap  was  striking. 
Professor  Titchener  ( 19)  deems  such  cases  of  sufificient  importance 
to  bring  to  the  support  of  the  Helmholtz  theory  of  hearing. 
He  says : 

"Cases  occur  in  which  the  range  of  hearing  is  normal,  but  the 
tonal  scale  is  not  continuous ;  there  are  tonal  gaps,  large  or  small, 
parts  of  the  scale  where  the  patient  is  completely  deaf  to  tonal 
stimuli,  though  he  can  perfectly  well  hear  the  cases  above  and  below." 

The  sources  of  error  in  a  problem  of  pitch-discrimination  are  so 
great  and  insistent  that  successive  investigators  of  the  same  problem 
are  fully  justified  in  a  patient  struggle  to  overcome  them  with  pro- 
gressive insight.  In  reading  the  various  reports  on  the  subject,  one 
cannot  help  being  impressed  with  the  fact  that  very  few,  if  any, 
of  the  investigators  fully  realized  the  significance  of  the  many  im- 
portant variables  which  could  easily — and  doubtless  did — vitiate  the 
results.  The  disturbing  factors,  due  to  faulty  apparatus  and  inade- 
quate procedure,  mentioned  by  Professor  Seashore  in  his  preliminary 
report  (13),  suggest  the  seriousness  of  the  problem.  From  my 
own  experience  I  am  convinced  that  his  statement  in  regard  to 
these  factors  is  in  no  way  exaggerated.  Rather,  it  has  not  been 
made  sufficiently  emphatic.  The  danger  of  false  criteria  entering 
into  the  judgments  of  the  most  conscientious  observer,  either  con- 
sciously or  unconsciously,  can  scarcely  be  realized  by  one  who  has 
not  encountered  them  first-hand.  The  danger  of  identification, 
alone,  is  sufficient  to  make  the  investigator  very  cautious. 

Apparatus  and  Method. — In  this  investigation  the  measurements 


122  THOMAS  F.   VANCE 

were  made  at  six  different  levels  in  the  register;  namely,  64,  128, 
256,  1024,  and  2048  v.d.  The  tones  were  produced  by  the  best  grade 
of  Kohl  tuning  forks.  For  128,  256,  512,  and  1024  v.d.  Helmholtz 
resonators  were  used;  the  forks  of  2048  v.d.  were  mounted  on 
resonator-boxes ;  while  resonance  for  64  v.d.  was  produced  by  ex- 
tending the  Helmholtz  resonator  for  128  v.d.  For  64  v.d.  a  second 
set  of  forks  was  found  to  be  more  satisfactory  at  a  later  stage  of  the 
experiment.  These  were  made  of  round  tool  steel,  12  mm.  in  diame- 
ter. The  prongs  were  30  cm.  in  length  and  carried  hard  rubber 
discs  10  cm.  in  diameter. 

The  sounder  was  a  simple  device  consisting  merely  of  a  lead 
pipe  about  one  inch  in  diameter  with  one  end  bent  into  the  form  of 
a  circle  for  the  base,  and  the  other  in  the  shape  of  a  U  at  right 
angles  to  the  base.  The  U-end,  when  covered  with  several  thick- 
nesses of  rubber,  made  a  sounder  of  the  required  elasticity  and 
softness.  The  placing  of  the  sounder  on  leather  sand-bags  resting 
on  a  heavy  metal  stand  eliminated,  in  large  part,  the  accessory  noise 
of  the  blow.  The  forks  of  the  four  central  octaves  were  energized 
by  striking  the  middle  of  the  prong  upon  the  sounder ;  the  forks  of 
2048  v.d.  were  struck  as  lightly  as  possible  with  a  felt-hammer; 
while  those  of  64  v.d.  were  set  into  vibration  by  striking  them  on 
the  sand-bags. 

To  mistune  the  variable  fork,  in  every  case  except  those  of  the 
lower  limit,  a  screw  was  inserted  in  the  end  of  each  prong  and  to 
these  were  attached  nuts,  varying  in  weight,  to  give  the  desired  pitch. 
Such  a  device  is  a  decided  improvement  over  the  method  of  sliding 
weights,  inasmuch  as  the  latter  may  allow  a  slight  change  in  posi- 
tion, with  a  corresponding  change  in  pitch,  during  the  course  of  the 
experiment.  This  is  especially  true  of  the  smaller  forks.  At  64  v.d. 
variation  in  pitch  was  secured  by  shifting  the  discs,  which  were 
firmly  attached  to  the  forks  by  large  set  screws.  At  each  of  the 
steps  the  successive  differences  of  one,  two,  three,  five,  and  eight 
vibrations  were  chosen — a  range  which  was  found  to  be  sufficient 
for  all  but  one  or  two  observers.  All  of  the  forks  were  tuned  to  an 
accuracy  of  five-hundredths  of  a  vibration  per  second. 

The  mode  of  procedure  followed  the  plan  suggested  by  Professor 
Seashore  in  his  preliminary  report  (13)  in  almost  every  respect, 
in  the  four  central  octaves  where  it  was  possible  to  do  so.  A  most 
careful  attempt  was  made  to  keep  the  tones  at  a  constant  intensity 


VARIATION  IN  PITCH  DISCRIMINATION  123 

without  resorting  to  the  uniformity  of  mechanical  devices.  The  ex- 
perimenter simply  relied  on  the  accuracy  of  his  own  hand  and  ear 
in  presenting  the  forks  in  such  a  way  that  the  tones  would  be  of 
equal  strength.  If  at  any  time,  through  a  lapse  on  the  part  of  the 
experimenter,  the  difference  of  intensity  seemed  pronounced,  the 
trial  was  repeated.  Mechanical  devices  are  particularly  unsatisfac- 
tory in  that  the  difference  of  intensity  which  is  practically  certain  to 
occur,  be  it  ever  so  slight,  is  constant  and  might  thus  become  a 
criterion  for  identification.  In  the  method  of  presentation  by  hand, 
this  source  of  error  is  eliminated.  The  ideal  presentation  is  that 
in  which  the  tones  are  just  loud  enough  to  be  heard  without  a  strain 
of  the  attention,  and  extreme  care  was  taken  throughout  to  guage 
the  tones  by  this  standard.  The  duration  of  each  tone,  as  well  as 
the  time-interval,  was  approximately  one  second.  Whether  the 
constant  or  the  variable  tone  should  be  presented  first,  was  decided 
by  a  key  which  had  been  arranged  first  by  chance  and  then  revised 
to  the  extent  that  the  same  order  could  be  followed  no  more  than 
three  times  in  succession,  and  that  in  one  hundred  tests  the  two 
possible  sequences  should  have  the  same  frequency.  The  observers 
in  every  case  were  required  to  render  their  judgments  in  terms  of 
"second  tone  lower",  or  "second  tone  higher",  in  accordance  with 
the  method  of  right  and  wrong  cases.  No  doubtful  judgments  were 
allowed;  when  the  observer  felt  uncertain  after  repeated  tests  he 
was  simply  requested  to  guess.  As  a  rule  each  individual  experiment 
was  given  but  once,  but  whenever  disturbances  of  any  sort,  either 
objective  or  subjective,  were  noted,  the  experiment  was  repeated. 
Observers  were  instructed  to  trust  the  first  impression.  Except  with 
the  lowest  tones,  where  the  judgments  were  given  orally  and  were 
then  recorded  by  the  experimenter,  the  observers  themselves  kept 
the  record  by  simply  writing  H  or  L  as  an  abbreviation  of  the  judg- 
ments "higher"  or  "lower."  With  one  observer,  however,  the  re- 
sponse was  oral  throughout  because  attention  to  the  writing  caused 
too  much  of  a  distraction.  At  least  one  hundred  judgments  were 
recorded  at  each  level,  but  many  observers  required  a  consider- 
ably larger  number  before  their  thresholds  could  be  satisfactorily 
determined.  No  series  of  observations  extended  long  enough  to 
cause  any  disturbing  fatigue.  The  monotony  of  the  experiment  was 
broken  at  intervals  by  the  checking  of  the  record  and  by  the  adjust- 
ing of  the  forks.    Fatigue  caused  previous  to  the  experiment  could 


124  THOMAS  F.   VANCE 

not  be  very  well  controlled  as  the  observers  had  to  be  taken  at  times 
which  best  suited  their  convenience.  The  tests  were,  however,  fairly 
well  distributed  throughout  the  hours  of  the  day  and  those  observers 
who  did  come  at  a  late  hour  were  always  dismissed  if  they  felt 
fatigue  to  a  degree  which  they  thought  might  interfere  with  their  best 
work.  The  experiment  was  conducted  in  the  sound-proof  room  and 
in  every  instance  the  observers  were  tested  individually  so  that  dis- 
tractions of  an  objective  character  were  reduced  to  conditions  con- 
nected only  with  the  actual  experiment. 

The  experimental  control  was  naturally  most  difficult  at  64  v.d. 
The  large  size  of  the  forks  not  only  made  them  more  difficult  to 
handle  but  also  increased  the  possibility  of  overtones.  Still  another 
problem  was  presented  in  obtaining  sufficient  resonance  for  these 
tones  of  low  intensity.  Overtones  were  especially  distracting  with 
the  first  pair  of  forks  that  were  used,  but  it  was  possible  to  over- 
come them  to  some  extent  by  setting  the  forks  in  heavy  handles  of 
iron  and  by  putting  heavy  rubber  bands  upon  the  prongs.  Yet  the 
increased  weight  added  to  the  difficulty  of  handling.  Two  different 
methods  were  tried  with  these  forks;  namely,  bringing  the  forks 
to  the  openings  of  the  resonators,  described  above,  and  presenting 
them  to  the  ear  of  the  observer  without  the  aid  of  a  resonator. 
Both  of  these  methods  are  unsatisfactory.  The  resonator  scarcely 
makes  the  tones  loud  enough  to  make  the  judgment  one  of  cer- 
tainty, and  it  is  difficult  for  the  experimenter  to  present  the  tones 
so  that  they  are  of  equal  intensity.  Holding  the  forks  to  the  ear 
has  the  advantage  of  making  the  tones  louder,  but  here  again  the 
variable  of  intensity  is  left  uncontrolled,  and  the  possibility  is  open 
to  the  observer  for  obtaining  clues  from  the  position  of  the  fork, 
from  timbre,  and  from  noises  caused  by  movements  in  presentation. 
The  fact  that  the  tones  could  be  distinctly  heard  by  the  second  method 
gave  it  the  preference.  But  when  the  results  were  compared  with 
those  obtained  for  128  v.d.  the  thresholds  seemed  abnormally  large. 
This  pair  of  forks  was  therefore  discarded  for  the  forks  with  the 
discs,  which  were  found  to  answer  the  purpose  much  better,  for  at 
least  three  reasons ;  namely,  they  were  freer  from  overtones,  the 
tones  were  louder  and  clearer  because  of  the  increased  vibratory 
surface  offered  by  the  discs,  and  they  were  neither  so  heavy  nor 
so  long,  which  facilitated  handling  very  materially.  With  these 
forks  the  method  of  presentation  to  the  ear  was  adopted,  but  on 


VARIATION  IN  PITCH  DISCRIMINATION  125 

account  of  the  louder  tone  it  was  possible  to  hold  the  forks  fartlicr 
from  the  ear.  Being  also  lighter  in  weight,  they  could  be  energized 
in  a  more  uniform  manner,  and  it  was  easier  to  bring  them  more 
nearly  to  the  same  point  opposite  the  ear ;  thus  the  variable  of  inten- 
sity and  direction  of  source  could  be  more  adequately  controlled.  An 
opportunity  was  not  offered  for  the  retesting  of  all  individuals  whose 
thresholds  had  been  determined  by  the  first  pair  of  forks,  but  in 
most  cases  where  a  second  was  possible,  somewhat  lower  thresholds 
were  obtained. 

No  particular  comment  in  regard  to  the  forks  of  128  and  256  v.d. 
is  necessary.  They  were  energized  and  presented  to  the  resonators 
with  the  conditions  of  duration,  time-interval,  and  intensity  care- 
fully controlled.  In  each  case  the  tones  were  perfectly  clear  and 
distinct.  The  forks  producing  these  tones  held  up  long  enough  to 
allow  five  individual  experiments  without  restriking.  But  the  con- 
trol was  not  quite  so  satisfactory  at  1024  v.d.  The  forks  at  this 
level  would  vibrate  with  sufficient  energy  for  only  two  tests.  A  more 
forceful  blow  was  also  required,  and  it  was  necessary  to  bring  them 
very  close  to  the  small  resonators,  indeed  so  close  that  they  nearly 
touched  it.  All  this,  of  course,  made  it  more  difficult  for  the  ex- 
perimenter to  maintain  a  constant  intensity.  Again,  the  piercing 
character  of  the  tone  was  annoying  to  some  observers.  The  tones 
produced  by  forks  of  128,  256,  and  512  v.d.  were  not  heard  by  the 
observers  except  when  reinforced  by  the  resonators.  But  the  1024 
v.d.  forks  gave  a  high  piercing  tone  before  being  presented  to  the 
resonator.  The  observer,  as  much  as  possible,  ignored  this  tone  and 
concentrated  his  attention  on  the  tones  as  they  were  intensified  by 
the  resonators. 

In  the  upper  limit,  the  method  was  necessarily  quite  different. 
The  small  resonator-boxes  on  which  the  forks  were  mounted  were 
held  in  the  hand ;  the  one  fork  was  struck  and  dampened,  and  then 
the  second  in  close  succession.  So  delicate  a  stroke  was  necessary 
to  produce  a  tone  that  the  noise  of  the  blow  was  but  a  slight  dis- 
traction, if  any.  It  was  extremely  difficult,  how^ever,  to  keep  the 
intensity  constant.  To  eliminate  discrimination  of  the  direction  of 
source,  the  position  of  the  left  hand  was  shifted  to  bring  the  forks 
to  exactly  the  same  place  before  they  were  energized. 

Of  the  fifty  observers  who  made  this  study  possible  by  giving  it 
their  time  and  thought,  thirty-three  were  members  of  the  elemen- 


126  THOMAS  F.   VANCE 


TABLE 

/.     A 

bsolnte  diff 

erentia 

/  threi 

holds 

Obs. 

64 
T    I 

v.d. 

128 

v.d. 

256  V 

•d. 

512 

/.d. 

1024  V 

.d. 

2048 

v.d. 

n.v. 

T    m.v. 

T    m.v. 

T    m.v. 

T    m.v. 

T    m.v. 

I 

2.5 

0.9 

1.9 

0.5 

0.8 

0.6 

0.7 

I.I 

3-3 

.0 

5-3 

0-4 

2 

3.5 

0.1 

0.8 

0.6 

0.6 

0.8 

I  0 

0.8 

2.2 

I.I 

2.5 

3-2 

3 

4 
5 
6 

3-3 

0.1 

0.6 

0.8 

0.7 

0.7 

0.8 

1.0 

2.5 

.8 

5-6 

O.I 

30 

0.4 

1.5 

0.1 

2.2 

0.8 

2.3 

0.5 

I.I 

2.2 

3-5 

2.2 

1.6 

4.0 

0.6 

1.3 

0.1 

I.I 

0.3 

0.9 

0.9 

4.1 

.8 

7-3 

0.7 

0.7 

0.8 

0.6 

1.2 

0.6 

2.4 

-9 

7 
8 

4.0 

0.6 

0.7 

0.7 

1.2 

0.2 

1-7 

0.1 

3-5 

.2 

6-7 

1.0 

I.O 

2.4 

1-5 

0.1 

1.4 

0.0 

1.8 

0.0 

3-7 

•4 

6.5 

0.8 

9 

6.4 

3.0 

2.7 

1-3 

0.7 

0.7 

1-7 

0.1 

5-3 

2.0 

6.5 

0.8 
0.8 

10 

1-5 

1.9 

1.4 

0.0 

I.I 

0-3 

1.8 

00 

2.4 

-9 

4.9 

II 

2.0 

1-4 

0.8 

0.6 

1-5 

0.1 

1.0 

0.8 

3-9 

.6 

5-6 

0.1 

12 

3-7 

0.3 

0.7 

0.7 

1-5 

0.1 

2.4 

0.6 

4-3 

1.0 

3-5 
6.7 

2.2 

13 
14 

i6 

1-5 

1.9 

1.0 

0.4 

0.7 

0.7 

2.0 

0.2 

3-8 

•5 

1.0 

4.0. 

0.6 

2.7 

1-3 

1.8 

0.4 

2.2 

0.4 

5-0 

1-7 

lO.O 

4-3 

3.0 

0.4 

1.4 

0.0 

2.1 

0.7 

4.4 

2.6 

6.4 

3-1 

8.8 

3-1 

3-4 

0.0 

1.3 

0.1 

0.6 

0.8 

0.8 

1.0 

2.2 

I.I 

^•^ 

2.7 

17 
i8 

2.0 

1.4 

I.I 

0.3 

2.9 

1.5 

5.0 

3.2 

5-1 

1.8 

7.6 

1-9 

0.7 

2.7 

1.0 

0.4 

2.0 

0.6 

06 

1.2 

0.8 

2.5 

5-8 

0.1 

19 

20 

5-2 

1.8 

0.6 

0.8 

I.I 

0.3 

0.8 

1.0 

4-1 

0.8 

9-7 

4.0 

1.0 

2.4 

1.0 

0.4 

0.7 

0.7 

1.2 

0.6 

H 

.1 

6.1 

0.4 

21 

3-8 

0.4 

2.3 

0.9 

1.6 

0.2 

1-7 

0.1 

3-6 

•3 

5-5 

0.2 

22 

2.5 

0.9 

0.8 

0.6 

1.0 

0.4 

1.3 

0.5 

2.0 

1-3 

3-0 

2.7 

23 

2.0 

0.6 

1-3 

0.1 

1.4 

0.4 

6.8 

3.5 

5-5 

0.2 

24 

6.4 

3-0 

1-5 

0.1 

I.I 

0.3 

1.5 

0.3 

2.0 

1-3 

25 

4.0 

0.6 

2.0 

0.6 

2.5 

I.I 

2.5 

0.7 

2.4 

•9 

4-4 

1-3 

26 

3.0 

0.4 

0.7 

0.7 

1.0 

0.4 

1.9 

0.1 

1.8 

1.5 

5-8 
3-6 

0.1 

27 

4-7 

1.3 

0.7 

0.7 

1-5 

0.1 

1-7 

0.1 

2.1 

1.2 

2.1 

28 

3-4 

0.0 

0.6 

0.8 

0.8 

0.6 

I  I 

0.7 

2.3 

1.0 

3-2 

2-5 

29 

2.4 

1.0 

2.1 

0.7 

1.5 

0.1 

1.6 

0  2 

8-4 

^•0 

10.2 

4-5 

30 

2.5 

0.9 

2.4 

1.0 

1-3 

0.1 

1.4 

04 

4-1 

.8 

5-7 

0.0 

31 

6.4 

3-0 

2.4 

1.0 

2.0 

0.6 

1.5 

0.3 

3-9 

.6 

3.0 

2-7 

32 

2.4 

1.0 

1.0 

0.4 

1.0 

0.4 

I.I 

0.7 

2.2 

I.I 

4-6 

I.I 

33 

1-7 

0.3 

1.4 

0.0 

2.7 

0.9 

3-2 

I 

8.8 

3-1 

34 

3-3 

0.1 

1.5 

0.1 

1-5 

0.1 

1.4 

0.4 

2.5 

0.8 

4-9 

0.8 

35 

6.4 

3.0 

I.I 

0.3 

1-7 

0.3 

1.0 

0.8 

6.4 

3-1 

9-9 

4.2 

36 

8.8 

5.4 

I.I 

0.3 

0.8 

0.6 

2.2 

0.4 

3-5 

•2 

4.8 

0.9 

37 

3.0 

0.4 

1-5 

0.1 

1.4 

0.0 

2.6 

0.8 

4.4 

I.I 

10.2 

4-5 

38 

0.7 

2.7 

0.6 

0.8 

0.7 

0.7 

2.1 

0.3 

1.6 

1-7 

3-7 

2.0 

39 

7-2 

3-8 

4.1 

2.7 

3-2 

1.8 

1.6 

0.2 

7-6 

4-3 

40 

0.9 

0.5 

1.2 

0.2 

0.9 

0.9 

0.7 

2.6 

4-3 

1-4 

41 

2.4 

1.0 

0.8 

0.6 

0.7 

0.7 

2.1 

0.3 

1.8 

1-5 

3-5 

2.2 

42 

4.0 

0.6 

2.0 

0.6 

3-2 

1.8 

4.9 

3-1 

7.0 

7.0 

1-3 

43 

1.3 

2.1 

0.8 

0.6 

0.7 

0.7 

I.I 

0.7 

1.8 

1-5 

5-3 

0.4 

44 

3-0 

0.4 

I.I 

0.3 

0.4 

1.0 

1.2 

0.6 

2.6 

•7 

3-0 

2-7 

4S 

3.1 

0.3 

1-4 

0.0 

1-5 

0.1 

1.4 

0.4 

3-2 

.1 

8.0 

2.3 

46 

1.4 

0.0 

1.3 

0.1 

2.6 

0.8 

2.7 

.6 

47 

30 

0.4 

1.2 

0.2 

1.6 

0.2 

1.7 

0.1 

2.4 

0.9 

48 

3.0 

0.4 

1-4 

0.0 

I.I 

0.3 

0.8 

1.0 

2.7 

.6 

49 

5.0 

1.6 

4.0 

2.6 

2.5 

I.I 

6.1 

4-3 

50 

i..^ 

2.1 

1.0 

0.4 

0.7 

0.7 

1.0 

0.8 

0.9 

2.4 

1.2 

4-5 

Mean    3.4 

1.5 

1-4 

.57 

1.4 

.5 

1.8 

.76 

3-3 

1-31 

5-7 

1.56 

Median    300 

1.2 

1-3 

1.5 

3-0 

5-5 

VARIATION  IN  PITCH  DISCRIMINATION 


TABLE  II. 

Relative  differential  thr 

esholds 

Obs.     64 

v.d. 

128  v.d. 

2S(j  v.d. 

512  v.d. 

1024  v.d. 

2048  v.d. 

I 

•31 

.12 

.03 

.01 

•03 

,02 

2 

.44 

•05 

.02 

.02 

.02 

.01 

3 

.41 

.04 

.02 

.02 

.02 

.02 

4 

.38 

.09 

.07 

.04 

.01 

.01 

5 

•50 

.08 

.03 

.01 

.03 

.03 

6 

.04 

•03 

.02 

.02 

7 

•50 

.04 

.04 

.03 

.03 

•03 

8 

.13 

.09 

.04 

■03 

•03 

•03 

9 

.80 

.17 

.02 

•03 

.04 

.03 

10 

.19 

.09 

•03 

.03 

.02 

.02 

II 

.25 

.05 

.05 

.02 

.03 

.02 

12 

.46 

V04 

•05 

.04 

.03 

.01 

13 

.19 

.06 

.02 

.03 

.03 

•03 

14 

•50 

.17 

.06 

.03 

.04 

.04 

15 

.38 

.09 

.07 

.07 

.05 

.03 

16 

•43 

.08 

.02 

.01 

.02 

.01 

17 

.25 

.07 

.09 

.08 

.04 

.03 

18 

.09 

.06 

.06 

.01 

.01 

.02 

19 

.65 

.04 

.03 

.01 

•03 

.04 

20 

.13 

.02 

.02 

.02 

.03 

.02 

21 

.48 

.14 

.05 

•03 

■03 

.02 

22 

.31 

•05 

.03 

.02 

.02 

.01 

23 

.13 

.04 

.02 

•05 

.02 

24 

.80 

.09 

.03 

.02 

.02 

.02 

25 

•50 

.13 

.08 

.04 

.02 

.02 

26 

.38 

.04 

.03 

•03 

.01 

.02 

27 

.59 

.04 

•05 

•03 

.02 

.01 

28 

.43 

.04 

.03 

.02 

.02 

.01 

29 

•30 

.13 

.05 

.03 

.06 

.04 

30 

.31 

.15 

.04 

.02 

•03 

.02 

31 

.80 

.15 

.06 

.02 

.03 

.01 

32 

•30 

.06 

.03 

.02 

.01 

.02 

33 

.11 

.04 

.04 

•03 

•03 

34 

.41 

.09 

.05 

.02 

.02 

.02 

35 

.80 

.07 

•05 

.02 

.05 

.04 

36 

.11 

.07 

•03 

•03 

•03 

.02 

37 

.38 

.09 

.04 

.04 

.03 

.04 

38 

.09 

.04 

.02 

•03 

.02 

.01 

39 

.90 

26 

.10 

.03 

.06 

40 

.06 

.05 

.01 

.01 

.02 

41 

.30 

•05 

02 

.03 

.01 

.01 

42 

•50 

.13 

.10 

.08 

•03 

43 

.16 

.05 

.02 

.02 

.01 

.02 

44 

.38 

.07 

.01 

.02 

.02 

.01 

45 

.39 

.09 

.05 

.02 

•03 

•03 

46 

.09 

.04 

.02 

.02 

47 

.38 

.08 

.05 

•03 

.02 

48 

.36 

.09 

•03 

.01 

.02 

49 

.63 

■25 

.08 

.10 

50 

.16 

.06 

.02 

.02 

.01 

.01 

Average 

.4 

.09 

.04 

•03 

.03 

.02 

,28  THOMAS  F.   VANCE 

tary  class  in  psychology  in  the  University,  sixteen  others  were  ad- 
vanced students  in  psychology,  and  one  other  a  member  of  the  staff 
in  psychology.  It  is  important  to  note  that  the  fifty  represent  a 
selected  group.  The  thirty-three  from  the  elementary  class  were 
chosen  from  a  class  of  one  hundred  or  more  because  their  differen- 
tial thresholds  at  435  v.d.  were  less  than  8  v.d.,  as  determined  from  a 
test  given  to  the  class  for  purposes  of  demonstration.  The  advanced 
students  had  likewise  shown  in  previous  tests  that  their  thresholds 
for  discrimination  of  pitch  were  easily  less  than  8  v.d.  Their 
closer  association  with  the  work  in  the  department  of  psycholog>' 
also  tended  to  make  them  slightly  better  as  a  group  than  the  elemen- 
tary students.  This  basis  of  selection  must  be  borne  in  mind  in 
the  consideration  of  the  results,  for  our  composite  curve  is  not  an 
average  curve;  it  is  superior  to  the  average.  It  was  gratifying  to 
find  that  all  of  the  observers  took  keen  interest  in  the  problem  and 
made  a  sincere  effort  to  give  the  work  their  best  attention.  Their 
knowledge  of  the  fact  that  they  were  chosen  because  of  their 
former  good  record  helped    them  to  maintain  an  interest. 

RESULTS 

The  Composite  Curves. — Table  I  includes  the  individual  thresh- 
olds in  terms  of  the  absolute  difference  of  vibrations  for  the  six 
points  in  the  range.  The  odd  numbers  of  the  observers  refer  to 
women,  and  the  even,  to  the  men.  The  thresholds  are  given  in 
column  T,  and  the  mean  variation  in  column  m.v.  At  the  foot  of 
the  table  are  the  mean,  the  median,  and  the  mean  variation  of  the 
group.  In  Table  II  the  same  records  are  reduced  to  the  relative 
threshold  expressed  in  terms  of  the  fractional  part  of  a  whole 
tone,  at  the  respective  levels.  The  figures  in  italics  at  the  head 
show  the  number  of  vibrations  in  a  whole  tone  at  each  of  these 
respective  levels.  The  record  of  Table  I  is  shown  graphically  in 
Fig.  I  and  that  of  Table  II  in  Fig.  2.  By  an  error  the  decimal 
point  was  left  out  before  each  of  the  numbers  i,  2,  3,  and  4,  in  Fig.  2. 

There  is  evidently  no  essential  difference  between  the  mean  and 
the  median  curves;  they  run  practically  parallel  throughout  their 
course,  coming  a  little  closer  together  at  256  v.d.  than  at  any  other 
point.  But  inasmuch  as  the  mean  allows  the  extremes  an  influence 
out  of  proportion  to  their  importance,  the  median  must  be  con- 
sidered the  truer  representative  figure. 


VARIATION  IN  PITCH  DISCRIMINATION 


129 


" 

' 

- 



-^ 

^_ 

.__ 

'/ 

'*\\ 

^^,, 

^ 

•«^. 

vs 

-rr 

TT^ 

-^ 

*c. 

— 

— Jt"" 

. — 

— 

•zzl^'" 

Mifct  H9  iSi.  iiJ-  "i-i  i.»t 

Fig.  I.     Mean,  median,  and  mean  variation — absolute   (Table  I). 


4»  &l       '  ib.%  aJl 

Fig.  2.    Mean — relative  (Table  II). 


su 


Soli 


The  average  capacity  of  discrimination,  as  measured  in  terms  of 
absolute  difference,  is  practically  the  same  for  128  and  256  v.d.  From 
this  central  register  the  curves  rise  slowly  to  512  v.d.,  from  which 
begins  a  rapid  rise  that  becomes  even  more  rapid  from  1024  on  up  to 
2048  v.d.  The  curve  of  mean  variation  (Fig.  i)  follows  the  general 
trend  of  the  composite,  which  means  that  the  thresholds  for  this 
group  of  fifty  form  a  more  compact  grouping  in  the  central  register, 
while  at  both  the  upper  and  the  lower  limits  they  are  more  widely 
separated. 

The  relative  curve  declines  rapidly  at  first  and  then  very  grad- 
ually, reaching  its  lowest  point  at  2048  v.d.  In  other  words  discrim- 
ination of  pitch,  as  measured  in  fractional  parts  of  a  whole  tone, 
decreases  somewhat  abruptly  from  64  to  128  v.d.,  but  very  slowly 
from  that  point  to  the  upper  limit  of  the  range  studied.  In  the 
relative  curve  the  minimal  value  is  at  2048  v.d.  which  is  the  region 
of  the  maximal  value  in  the  curve  of  absolute  difference. 


130  THOMAS  F.   VANCE 

The  absolute  difference  of  vibration  frequency  has  been  adopted 
as  the  vehicle  of  expression  in  this  report,  for  the  reason  that  it  is 
slightly  more  concrete  and  brings  out  the  individual  differences  more 
strikingly.  Its  true  relation  to  the  relative  must,  however,  be  kept 
in  mind. 

The  curves  represent  with  a  high  degree  of  accuracy,  it  is  be- 
lieved, the  average  capacity  of  a  group  of  observers  such  as  have 
had  a  part  in  this  study.  But  there  is  little  doubt  that  the  form  of 
the  curves  has  been  influenced,  to  some  extent,  by  certain  factors 
other  than  those  of  actual  discrimination  of  pitch.  There  are  ob- 
jective factors  which  could  not  be  perfectly  controlled  and  which  in 
some  cases  have  led  to  confusion,  but  in  other  cases  have  resulted  in 
identification.  The  former  necessarily  raised  the  threshold,  while 
the  latter  lowered  it.  The  subjective  variables  of  attention  and 
practice  are  important  inasmuch  as  attention  is  seldom  at  is  best 
and  then  only  for  short  duration,  and  the  degree  of  practice  might 
always  be  greater.  The  thresholds  are  therefore  not  quite  as  low 
as  they  would  be  under  the  most  ideal  conditions. 

With  tuning  forks,  it  is  impossible  to  produce  as  satisfactory  a 
tone  at  the  extremes  as  in  the  central  register.  Discrimination  of 
pitch  at  64  and  at  2048  v.d.  is  thus  made  most  difficult  and  the 
observer  has  a  tendency  to  pick  up  other  criteria  than  pitch  upon 
which  to  base  his  judgments.  Differences  of  intensity,  change  in 
the  direction  of  the  source  of  sound,  and  noises  accompanying  the 
control  of  the  experiment  are  the  chief  factors  which  cause  distur- 
bance. They  lead  to  confusion,  rather  than  to  identification,  because 
the  method  used  necessitated  their  approximately  equal  distribution 
between  the  higher  and  the  lower  tones ;  that  is  to  say,  that  they 
occurred  in  a  chance  order,  were  therefore  unpredictable,  and  con- 
sequently could  not  be  used  as  safe  criteria  for  accurate  judg- 
ments; for  example,  if  an  observer  was  inclined  to  judge  the  more 
intense  tone  the  higher,  there  would  be  an  increased  probability  of 
error  whenever  the  lower  tone  happened  to  be  more  intense.  Had 
the  forks  been  energized  by  a  mechanical  device,  rather  than  by  the 
free  hand,  these  variables  would  have  been  constant  and  would  have 
become  a  means  of  identification,  rather  than  a  source  of  confusion. 
At  the  higher  limit  it  was  difficult  to  keep  the  tones  of  equal  loud- 
ness. The  tones  produced  by  the  small  forks  are  very  fine  and 
persistent,  and  a  slight  variation  in  the  forces  of  the  blow  produced 


VARIATION  IN  PITCH  DISCRIMINATION  131 

a  perceptible  change  in  the  intensity  of  the  tones,  which  was  often 
confusing.  Whether  or  not  the  greater  intensity  favored  a  judgment 
of  higher  or  lower  varied  with  the  individual.  For  some,  the  pitch 
being  nearly  equal,  the  louder  tone  was  considered  the  higher,  while 
for  others  the  reverse  experience  was  true. 

It  is  in  the  lower  limit,  however,  that  the  most  abrupt  rise  in  the 
threshold  is  to  be  found.  As  has  been  previously  mentioned,  various 
methods  of  presentation  were  given  a  trial,  but  none  of  them,  ex- 
cepting with  a  very  few  observers,  gave  results  which  were  compar- 
able with  those  obtained  at  128  v.d.  Only  two  observers  had  a 
lower  threshold  for  64  and  for  128  v.d.,  (Nos.  8  and  18).  For  ob- 
server No.  20  the  thresholds  for  the  two  tones  were  the  same,  while 
No's.  10,  13,  29,  30,  38,  and  50  were  the  only  remaining  ones  whose 
thresholds  for  64  v.d.  did  not  exceed  that  of  128  v.d.  by  more  than 
0.5  v.d.  In  other  words,  forty  observers  have  a  threshold  for  64 
which  is  more  than  one-half  of  a  vibration  higher  than  for  128  v.d. 
That  this  difference  would  have  been  less  had  it  been  possible  to  rule 
out  all  the  factors  of  confusion  is  probable. 

But  not  all  of  the  variables  cause  confusion.  Those  which  are 
constant  soon  come  to  be  associated  with  one  of  the  two  possible 
judgments  and  this,  in  time,  brings  about  a  lowering  of  the  threshold. 
Just  what  is  seized  upon  as  a  means  of  identification  one  cannot 
always  say.  The  auditory  capacity  of  analysis  is  very  keen  and  often 
the  slightest  variable  which  occurs  in  a  particular  setting  is  selected 
as  a  clue  for  the  proper  response.  Slight  variations  in  timbre  are 
among  the  most  frequent  sources  of  identification.  It  is  impossible 
to  make  two  forks  exactly  alike  and  the  unavoidable  structural 
difference  may  be  perceived  in  the  nature  and  composition  of  the 
overtones.  The  forks  of  the  lower  limit  are  particularly  susceptible 
to  variation  in  timbre.  If  these  differences  are  perceptible,  the  error 
of  identification  is  sure  to  appear.  Even  with  presentation  by  hand 
there  is  the  possibility  of  the  experimenter's  falling  into  some  charac- 
teristic habit  of  presenting  the  forks,  which  may  be  identified  eventu- 
ally. He  may  form  the  habit  unconsciously  of  striking  one  fork 
at  a  different  angle  from  that  of  the  other,  or  the  time-order  may 
have  some  constant  peculiarity  which  gives  a  clue. 

The  errors  due  to  identification  are  without  a  doubt  the  most 
serious  with  which  the  experimenter  has  to  contend.  But  in  an  ex- 
periment such  as  this  the  error  of  identification  is  usually  discover- 


132  THOMAS  F.   VANCE 

able  by  comparing  the  thresholds  of  one  level  with  those  of  the 
other  levels.  Whenever  an  observer  has  a  threshold  at  any  particular 
level  considerably  lower  than  the  tentative  norm  would  warrant,  the 
chances  are,  that  the  error  of  identification  has  had  a  part  to  play. 
The  recordof  No.  20  is  wanting  in  the  table  for  2048  v.d.  because  he 
had  discovered  some  criterion  other  than  pitch  upon  which  to  base 
his  judgments.  In  fact  he  made  nearly  a  perfect  record  with  a  differ- 
ence of  one  vibration, — a  lower  threshold' than  his  records  at  the 
other  levels  would  warrant.  Two  other  observers  had  a  similar 
experience  in  the  upper  limit,  but  when  the  method  was  slightly 
changed,  they  lost  their  clue  and  were  forced  to  rely  on  pitch.  In 
the  lowest  level  Nos.  28  and  40  were  influenced  in  some  way  by 
criteria  other  than  pitch,  the  latter  to  such  an  extent  that  his  results 
were  worthless.  As  has  been  said,  just  what  criteria  were  selected 
by  these  observers  is  not  known.  Their  introspections  fail  to  reveal 
them,  the  observers  contending  throughout — and  with  undoubted 
conviction — that  they  were  judging  on  pitch  alone.  Such  illus- 
trations show  that  the  experimenter  connot  be  too  careful  in  his 
attempt  to  keep  the  judgments  confined  to  pitch. 

The  subjective  variables  of  attention  and  practice  also  play  more 
important  roles  at  the  extremes  than  in  the  central  register.  To 
secure  a  low  threshold  at  these  levels  closer  attention  is  necessary 
and,  as  these  tones  are  rarely  heard,  the  degree  of  practice  is  much 
less  than  for  tones  of  the  central  register.  Practice  for  these  tones 
is  only  to  be  had  in  the  laboratory  as  they  are  seldom  used  in 
musical  compositions.  Observers  Nos.  2,  28,  47,  and  50  were  the 
only  ones  who  had  the  advantage  of  practice  for  these  extreme  tones 
and  their  thresholds  at  these  levels  are  all  below  the  average. 

Summing  up,  we  have  found  that  the  curve  of  pitch-discrimination 
shows  the  threshold  of  absolute  difference  to  be  keenest  from  128  to 
256  v.d.;  from  256  to  512  v.d.  it  takes  a  gradual  rise;  and  from  512 
to  2048  v.d.,  a  rapid  rise.  On  the  lower  side,  from  128  to  64  v.d.,  the 
rise  is  very  sudden.  As  expressed  by  the  curve  of  relative  difference, 
there  is  a  continual  decline  from  the  lower  to  the  higher  limit ;  this 
decline,  however,  is  very  rapid  from  64  to  128  v.d.,  much  less  pro- 
nounced from  128  to  256  v.d.,  and  from  256  to  2048  v.d.  the  curve 
becomes  very  nearly  a  straight  line.  It  will  be  of  interest  now  to 
comj^are  the  above  results  with  those  of  other  investigators. 

Comparative  Curves. — Figure  3  represents  the  composite  results 


VARIATION  IN  PITCH  DISCRIMINATION 


133 


Fig.  3.     Composite   curves    for    six   different    investigators — absolute. 

of  the  six  different  investigators  who  have  approached  the  problem 
by  the  same  general  method.  The  curves  of  Stiicker  (16),  Schaefer 
(10),  and  the  writer  show  considerably  higher  thresholds  than  those 
of  Luft,  Preyer  and  Meyer.  This  difference  may  be  explained.  In 
a  pioneer  work,  such  as  Preyer's  (7),  numerous  sources  of  error  as 
yet  undiscovered  must  have  had  much  influence  upon  the  results. 
His  low  thresholds  can  be  attributed,  in  some  degree  at  least,  to  the 
error  of  identification.  Since  this  error  may  creep  in  when  the  best 
grade  of  tuning  forks  is  used,  there  is  little  doubt  but  that  it  must 
have  played  an  important  role  with  the  tonmesser.  Furthermore 
this  instrument,  the  reed,  is  not  reliable  for  fine  pitch  differences. 
Luft's  (4)  values,  especially  at  the  extremes,  must  likewise  be  ques- 
tioned. Whenever  such  low  results  are  obtained  at  64  and  at  2048 
v.d.,  there  must  be  conclusive  evidence  that  they  are  not  due  pri- 
marily to  discrimination  of  pitch,  but  to  some  other  factor  which 
permits  of  identification.  Luft  has  given  no  such  proof.  Further- 
more, in  a  problem  of  this  kind,  the  method  of  minimal  change, 
which  he  used  is  unreliable,  as  Meyer  has  well  pointed  out,  in  that  it 
introduces  factors  other  than  those  of  pitch  and  the  threshold  value 
is  not  quite  comparable  to  the  threshold  value  in  our  method  of 
constant  stimuli.  Professor  Stumpfs  curve,  drawn  by  Meyer  (5), 
shows  exceptional  ability  and  is  probably  accurate.  The  low  thres- 
holds can  be  adequately  explained  by  the  less  extended  range,  by 
extraordinary  natural  capacity,  and  by  a  high  degree  of  training  in 


134  THOMAS  F.   VANCE 

experimental  work.  On  the  other  hand  it  should  be  kept  in  mind 
that  the  curves  of  Stiicker,  Schaefer,  and  the  writer,  represent  the 
results  of  a  much  larger  number  of  observers,  many  of  whom  do 
not  have  exceptionally  fine  capacity  for  discrimination  of  pitch.  The 
curves  are  therefore  on  a  much  higher  level  than  if  they  were  drawn 
exclusively  from  the  results  of  observers  who  had  unusually  fine 
ability. 

In  the  curves  of  Preyer,  Schaefer,  Meyer,  and  the  writer  the 
minimal  threshold  lies  somewhere  near  the  central  region ;  but  in  the 
other  two  discrimination  seems  to  be  the  best  in  the  lowest  level. 
With  Preyer  the  finest  capacity  is  at  500,  with  Luft  at  64,  with  Meyer 
at  600  (although  the  thresholds  for  200,  400,  and  600  are  practically 
equal),  with  Stiicker  at  73.4,  with  Schaefer  at  128,  and  with  the 
writer  at  256  v.d.  The  maximal  threshold  is  to  be  found  in  the 
highest  part  of  the  range  in  every  case.  The  second  maximum  lies 
with  Preyer,  ]\Ieyer,  Schaefer  and  the  writer  at  64  v.d. 

An  examination  of  these  curves  raises  the  question  as  to  the 
cause  of  the  variations.  Individual  differences  are,  of  course,  the 
principal  cause  but  the  nature  of  the  objective  control  is  undoubt- 
edly a  very  important  factor,  especially  at  the  extremes.  If  the 
apparatus  and  the  method  of  the  three  investigators,  who  had  a 
large  number  of  observers,  had  been  equally  refined  at  the  different 
steps,  these  grosser  differences  would  probably  not  have  occurred. 
As  it  is,  they  are  most  pronounced  at  the  extremes  where  the  con- 
trol was  the  most  difficult.  The  experimental  control  at  128,  256, 
and  512  v.d.  can  be  made  so  perfect  that  no  observer  will  be  able 
to  pass  consistent  judgments  on  any  criterion  other  than  pitch. 
For  this  reason  the  results  of  Stiicker,  Schaefer,  and  the  writer 
agree,  approximately,  within  this  region. 

Inasmuch  as  the  curves  take  the  same  general  direction,  the 
variations  in  the  upper  limit  are  about  what  would  be  expected 
when  one  considers  the  difficulties  to  be  encountered,  together  wnih. 
the  fact  that  one  of  the  experimenters  used  an  entirely  different 
apparatus.  But  from  130.5  to  73.4  v.d.,  Stiicker's  curve  continues 
in  the  same  general  direction  which  it  has  had  throughout  the  en- 
tire course,  while  the  other  two  curves  have  changed  their  direction. 
In  other  words,  Stiicker  found  the  absolute  difference  for  73.4  v.d. 
to  be  less  than  for  any  other  point  in  the  line,  while  both  Schaefer 
and  I  found  at  64  v.d.  the  second  maximum  which  is  noticeably 


VARIATION  IN  PITCH  DISCRIMINATION  135 

greater  than  for  any  other  point  except  at  2048  v.d.  Luft's  results 
seem  to  confirm  those  of  Stiicker,  but  Meyer's  curve,  as  well  as 
Preyer's,  shows  a  rise  at  the  lower  limit.  Indeed  the  ratio  between 
the  thresholds  of  Meyer  for  100  and  200  v.d.  is  very  similar  to  the 
ratio  between  the  thresholds  for  64  and  128  v.d.  obtained  by  Schaefer 
and  myself.  I  have  no  hesitancy  in  concluding,  therefore,  that  sen- 
sitiveness in  the  great  octave  is,  in  general,  not  so  keen  as  in  the  small 
octave.  But  for  reasons  already  given,  it  does  not  follow  that  the 
difiference  is  actually  as  great  as  the  numerical  results  of  this  study 
would  seem  to  indicate.  In  the  light  of  the  experience  of  the 
present  study,  however,  Stucker's  findings  in  the  lower  limit  must  be 
held  in  question.  It  seems  more  probable  that  his  observers  had 
learned'  to  make  judgments  on  some  criterion  other  than  pitch. 
Just  what  that  may  have  been  cannot  be  stated  definitely  as  that 
author  has  failed  to  give  any  detailed  account  either  in  regard  to 
method  or  to  apparatus.  It  is  only  known  that  the  tone  in  ques- 
tion was  produced  by  a  tuning  fork.  The  possibilities  of  error 
with  the  large  tuning  forks  are,  however,  sufficiently  great  to  warrant 
the  statement  that  Stucker's  low  record  is  due,  not  altogether  to 
discrimination  of  pitch,  but  that  secondary  criteria  have  been  op- 
erative in  giving  the  low  thresholds. 

Individual  Differences. — An  examination  of  Table  I  discloses  the 
fact  that  the  observers  may  be  classified  in  two  general  divisions.  In 
the  first  there  are  thirty-seven  whose  curves  follow  the  course  of 
the  composite  curve  in  that  the  smallest  values  are  to  be  found  in  the 
central  register  on  either  side  of  which  a  slow  or  a  rapid  rise  is  evi- 
dent. In  the  second  division,  are  thirteen  whose  curves  do  not  con- 
form to  any  general  type.  In  the  irregularity  of  the  curves  of  this 
second  division  lies  the  only  possible  evidence  of  gaps  which  this 
study  has  developed. 

The  curves  of  the  first  division  may,  in  a  general  way,  be  given 
a  three-fold  classification  ;  namely,  (i)  those  which  show  a  relatively 
low  threshold  at  some  point  in  the  central  region  and  relatively  high 
thresholds  at  the  extremes,  (2)  those  in  which  the  thresholds  are 
fairly  uniform  throughout  the  entire  range,  and  (3)  those  curves 
in  which  the  threshold  for  64  is  lower  than  for  2048  v.d. 

Division  I.— In  Figure  4  are  the  five  curves  of  the  first  group 
which  show,  the  most  strikingly,  the  relatively  low  thresholds  in  the 
central  register  and  the  higher  thresholds  at  the  extremes.     These 


136 


THOMAS  F.   VANCE 


^  Hd 


1348 


Fig.  4.  Individual  curves  of  observers  Nos.  5,  7,  9,  14,  and  27,  which 
show  relatively  low  values  in  the  central  region  and  high  values  at  the 
extremes.     The  solid  line  is  the  composite  curve  of  the  fifty  observers. 


curves  all  resemble  the  composite  more  or  less  closely.  At  the 
extremes,  however,  all  excepting  that  of  No.  27  rise  above  the  com- 
posite, but  in  the  central  region,  at  128,  256,  and  512  v.d.,  one-third 
of  the  fifteen  thresholds  pass  beneath  it.  The  normal  variation  of  the 
point  of  keenest  discrimination  is  well  illustrated  in  this  figure. 
Nos.  7  and  2y  made  the  best  record  at  128,  Nos.  9  and  14  at  256,  and 
No.  5  at  512  v.d.  In  fact,  all  but  one  of  the  entire  number  of  ob- 
servers made  their  lowest  record  at  one  of  these  central  levels. 

These  curves  represent  the  results  of  observers  who  were  the 
most  unreliable.  Very  few  of  these  values  indicate  the  physiological 
threshold.  One  could  not  say  that  the  high  values  at  the  extremes 
should  be  interpreted  to  mean  that  all  of  the  observers  in  question 
were  unable  to  perceive  smaller  differences  on  account  of  physio- 
logical incapacity.  It  is  much  inore  probable  that  the  difficulty  is 
psychological.  Individuals  of  this  type  do  not  adapt  themselves  so 
readily  to  new  situations  under  experimental  control.  When  new 
adjustments  must  be  made  their  work  is  relatively  poor  and  con- 
tinues on  a  low  plane  until  time  has  been  given  for  the  proper 
adjustment  after  which  their  work  may  be  on  a  par  with  that  of 
individuals  who  adapt  themselves  more  quickly  to  new  situations. 

iMgure  5  represents  the  results  of  the  six  individuals  who  are 
most  typical  of  the  second  group.  All  of  these  observers  are  men,  but 
they  are  not  of  equal  rank  in  previous  work  in  discrimination  of 


VARIATION  IN  PITCH  DISCRIMINATION 


137 


Fig.  5.  The  composite  curve  of  the  fifty  observers  and  the  individual 
curves  of  Nos.  2,  16,  22,  28,  44,  and  50,  which  are  characterized  by  a  high 
degree  of  uniformity  in  the  threshold  values  throughout  the  range. 


pitch.  Nos.  2,  32,  and  48  were  graduate  students  in  psychology  and 
were  trained  in  other  tests  of  discrimination;  with  the  remaining 
three,  however,  previous  training  was  very  limited.  The  striking 
difference  between  these  curves  and  those  of  the  former  group  is,  as 
would  be  expected,  with  reference  to  the  extremes.  The  values  for 
64  and  especially  for  1024  and  2048  v.d.  are  lower  than  in  curves  of 
the  first  type;  they  approach,  therefore,  a  more  uniform  level, — a 
goal  which  is  most  nearly  approximated  by  No.  48.  In  contrast  to 
the  former  group,  these  curves  fall  below  the  composite  at  practically 
every  point ;  only  four  values  are  actually  higher  than  the  composite, 
while  two  more  are  equal,  and  these  are  at  the  lower  limit.  From 
the  standpoint  of  consistency,  the  curves  of  Class  II  can  easily  be 
judged  the  better.  Observers  who  give  such  results  are  reliable. 
With  a  state  of  secondary  passive  attention,  they  are  able  to  meet 
the  new  situation  in  an  easy  and  natural  manner  and  are  little  dis- 
turbed by  unusual  difficulties  which  may  be  presented.  In  addi- 
tion, exceptional  ability  in  analyzing  a  problem  enables  them  to  select 
the  proper  element  or  elements  upon  which  to  base  their  judgments, 
even  though  there  be  disturbing  factors.  They  are  so  consistent  that 
the  experimenter  can  feel  a  high  degree  of  assurance  that  their 
records  represent  a  close  approach  to  the  physiological  threshold. 

The  curves  of  the  five  individuals  who  are  most  representative  of 
the  third  group  are  shown  in  Figure  6.  The  peculiar  character  of 
these  curves,  in  contrast  to  those  already  considered,  lies  in  the  lower 
limit.     Here  the  thresholds  are  very  much  lower  than  for  Class  I 


138 


THOMAS  F.  VANCE 


TVo.  17 

/vo  /J 

uo.  a 

iVa  £0 

- -//o  /O 


64  <ld 


TEST- 


IT*  » 


Fig.  6.  The  composite  curve  of  the  fifty  observers  and  the  individual 
curves  of  8,  lO,  13,  17,  and  20,  which  show^  relatively  low  values  at  the 
lower  limit  and  high  values  at  the  upper  limit. 


and  considerably  lower  than  they  are  for  Class  11.  But  in  the  upper 
extreme  the  curves  are  similar  to  those  of  the  first  group,  with  one 
exception, — the  curve  of  No.  17.  Indeed  the  average  results  of  these 
five  observers  form  a  curve  which  closely  approximates  Stiicker's 
curve,  the  essential  difference  being,  that  the  latter  is  tilted  at  a 
slightly  dift'erent  angle,  due  to  the  fact  that  Stiicker's  thresholds  at 
73.4  v.d.  are  lower  than  ours  and  higher  in  the  vicinity  of  2048  v.d. 
The  similarity  of  our  results  to  those  of  Stiicker  in  the  lower  ex- 
treme might  invite  the  same  criticism  which  we  advanced  against 
him.  It  might  be  said  that  our  low  threshold  at  64  v.d.  was  due  to  the 
discovery  of  some  variable  other  than  pitch  upon  which  the  judg- 
ment was  based.  There  is,  of  course,  the  possibility  that  this  oc- 
curred, but  reference  to  Figure  7,  in  which  the  composite  curves  of 
the  three  groups  may  be  compared,  leads  to  the  belief  that  such 
a  criticism  does  not  have  much  weight  with  respect  to  these  par- 
ticular observers.  It  is  to  be  observed  that  the  minimal  thresholds 
of  the  first  two  groups  lie  at  256  v.d.  with  a  gradual  rise  on  either 
side  of  this  point.  The  point  of  keenest  discrimination  for  Class 
III,  however,  lies  at  128  v.d.  with  here  again  a  rise  on  either  side 
proportional  to  that  which  we  find  in  the  other  two  groups.  In 
other  words,  the  form  of  the  latter  curve  from  64  to  256  v.d.  is 
similar  to  the  form  of  the  other  two  from  128  to  512  v.d.  We 
should  expect  to  find  a  higher  threshold  for  64  when  the  minimum  is 


VARIATION  IN  PITCH  DISCRIMINATION 


139 


t 

—  - 

— 

- 

- 

^ 

/   / 

.\__ 

■>'■'''    / 

— 

.T^i« 

X 
^ 

■- 

:=s=^ 

^X' eonipositc 

—  - —  ^.- 

-.— 

- 

" 

ISlasi  a 

(Elass  M 

Fig.  7.  The  composite  curves  of  the  fifty  observers  and  the  three  different 
classes. 

at  256  than  when  it  is  at  128  v.d.,  and  this  is  what  occurs.  With 
conditions  such  as  they  are,  we  are  incHned  to  regard  the  results  of 
this  class  of  observers,  at  64  v.d.,  as  fairly  accurate.  The  observers 
in  question  naturally  do  better  work  on  the  low  tones.  If  such  an 
interpretation  is  true,  it  would  not  be  just  to  say  that  the  curve  of 
Class  III  is  less  consistent  than  the  curve  of  Class  II;  each  rep- 
resents a  different  type  and  is  consistent  with  itself  throughout. 

There  are  still  to  be  considered  the  results  of  the  thirteen  ob- 
servers which  are  not  exactly  comparable  to  any  of  the  classes 
described  above,  because  of  certain  irregularities  occurring  in  their 
curves.  It  must  be  determined  whether  or  not  these  ridges  or  ele- 
vations may  be  explained  on  the  basis  of  daily  fluctuations,  in  which 
case  a  sufficiently  large  number  of  observations  would  result  in 
smooth  curves,  or  whether  the  variations  are  due  to  natural  weak- 
nesses for  the  regions  where  they  are  found.  The  extent  to  which 
this  latter  explanation  must  be  invoked,  indicates  an  answer  to  the 
question  of  the  frequency  of  gaps  in  the  registers  of  individuals  who 
have  apparently  normal  hearing. 

In  Table  I,  the  observers  who  have  such  curves  are  Nos.  4,  8, 
II,  12,  18,  19,  25,  38,  40,  41,  and  45.  It  will  be  noted,  however,  that 
at  no  place  are  the  deviations  from  the  normal  very  pronounced. 
All  of  them,  excepting  perhaps  one,  are  doubtless  due  to  certain 
factors  which  would  have  been  eliminated  by  a  large  number  of 
judgments.  Daily  variations,  the  relative  amount  of  practice,  and  the 
accuracy  with  which  the  increments  used  corresponded  to  the  true 


140  THOMAS  F.   VANCE 

thresholds,  are  the  most  important  factors  which  have  contributed 
toward  the  irregularities.  With  No.  5,  for  example,  the  experiment 
was  begun  at  256  v.d.,  so  that  the  greater  amount  of  practice  would 
give  the  neighboring  tones  the  advantage.  With  No.  11,  the  tone  of 
256  v.d.  was  first  tried  with  a  difference  of  2  v.d.,  which  was  too 
large,  resulting  in  an  almost  perfect  series.  Had  the  order  in  which 
these  differences  were  presented  been  reversed,  the  threshold  would 
probably  have  been  very  close  to  i  v.d.  Indeed,  a  number  of  these 
observers  were  given  additional  tests  to  determine  whether  or  not 
these  variations  from  the  normal  would  hold.  In  each  case  as 
Table  III  will  show,  the  curves  became  fairly  smooth. 

The  curve  of  No.  4  is  abnormal  at  1024  v.d.  in  its  relatively  low 
threshold  of  i.i  v.d.  During  an  experimentation  of  one  hour  he 
made  a  record  of  eighty-eight  per  cent,  on  two  hundred  judgments 
with  a  difference  of  2  v.d.  But  on  the  following  day,  a  difference  of 
I  v.d.  gave  only  fifty-two  per  cent,  of  the  right  cases.  A  larger 
number  of  observations  would  doubtless  have  resulted  in  a  threshold 
more  equal  to  that  of  the  tone  an  octave  lower. 

But  there  is  one  observer,  No.  18,  who  gives  some  evidence  of  a 

TASLE  III.  Irregular  results  which  additional  observations  have  corrected 
Observer   64  128  256 

19  5.2  0.6  I.I 

0.6  0.6 

41  2.4  0.8  0.7 

I.I  1.5 

1.8  2.2 

0.6  0.7 

I.I 
0.7  1-5 

slight  weakness  in  the  region  of  256  v.d.  His  threshold  at  this 
point  was  derived  from  four  hundred  judgments.  The  first  half 
of  the  number  with  a  difference  of  3  v.d.  gave  a  threshold  of  2.9 
v.d.,  while  the  second  half  with  a  difference  of  2  v.d.  gave  a  threshold 
of  2.3  v.d.  At  no  time  was  he  able  to  approach  a  threshold  of  i  v.d. 
On  the  other  hand,  with  the  tones  above  and  below,  he  made  low  and 
consistent  thresholds.  It  is  difficult  to  account  for  this  high  threshold 
at  256  v.d. ;  the  observer  himself  could  offer  nothing  as  a  basis  for 
explanation.  The  affective  element,  association  and  imagery,  and 
inherent  characteristics  of  volume  and  intensity  may  have  played 
varying  roles  in  causing  the  discrepancy.     At  any  rate  the  differ- 


35 

6.4 

38 

0.7 

12 

37 

5^2 

1024 

2048 

0.8 

4.1 

97 

I.I 

2.1 

1.8 

3-5 

1.8 

3-5 

I.I 

6.4 

9-9 

2.6 

2.1 

1.6 

37 

•9 

1.3 

2.4 

4-3 

3-5 

1.8 

Z-2, 

VARIATION  IN  PITCH  DISCRIMINATION  141 

ences    are   not    sufficiently   great    to    be    regarded    as    representing 
gaps. 

We  have  found,  then,  from  this  study  of  the  curves  of  discrimina- 
tion of  pitch  of  fifty  normal  observers  no  clear  evidence  of  tonal 
gaps.  The  grosser  irregularities  which  might  arouse  the  suspicion 
of  a  gap  are  due  to  certain  factors  which  have  not  been  perfectly 
controlled.  It  is  highly  probable  that  with  more  extended  observa- 
tions the  irregularities  would  have  been  eliminated.  It  must  be  kept 
in  mind,  however,  that  this  conclusion  has  reference  only  to  observers 
with  apparently  normal  auditory  capacity;  with  respect  to  indivi- 
duals whose  audition  is  unquestionably  recognized  as  pathological, 
this  study  has  nothing  to  offer. 

Relation  of  Musical  Training  and  Expression  to  Discrimination  of 
Pitch. — The  question  naturally  occurs  in  a  study  of  this  kind  as  to 
the  nature  and  extent  of  the  correlation  between  musical  education 
and  pitch-discrimination.  It  seemed  obvious  that  if  a  correlation 
existed  it  would  be  between  discrimination  and  musical  expression 
rather  than  between  discrimination  and  mere  technical  training.  The 
Pearson  method  of  rank  difference  was  used  to  determine  the 
correlation.  The  mean  of  the  six  levels  in  the  range  for  each  of 
thirty-eight  observers  gave  a  value  for  the  ranking  of  the  indi- 
viduals according  to  their  capacity  for  the  discrimination  of  pitch. 
The  records  of  the  remaining  twelve  were  not  included  as  most 
of  them  were  advanced  students  whose  greater  experience  in 
work  in  the  laboratory  might  possibly  put  them  in  a  slightly 
better  class,  while  with  one  or  two  others,  information  regarding 
their  musical  training  was  not  at  the  time  available.  The  ranking 
according  to  expression  was  not  quite  so  simple.  For  this  pur- 
pose an  evaluation  was  made  of  the  answers  to  the  question- 
naire, which  was  an  exact  duplicate  of  the  one  published  by  Professor 
Seashore  in  his  Preliminary  Report  (13).  To  recall,  there  are  three 
questions  under  the  topic  "Musical  Expression":  namely,  (i) 
Favorite  selections  you  can  sing  (by  ear?  by  note?),  (2)  Favorite 
selections  you  can  play  (by  ear?  by  note?),  (3)  Singing  or  playing 
in  public  (parts,  occasions,  etc.).  The  individuals  were  instructed  to 
give  as  specific  information  as  possible.  But  the  comparison  of  the 
two  functions  showed  no  correlation  whatever. 

It  was  still  believed,  however,  that  there  must  be  some  difference 
between  the  discriminating  capacity  of  those  who  seemed  to  be  the 


142 


THOMAS  F.   VANCE 


most  musical  and  those  who  appeared  to  be  the  least,  as  far  as 
previous  experience  was  concerned.  Again  the  questionnaire,  to 
which  reference  has  been  made  was  resorted  to,  but  this  time  the 
questions  were  designed  to  reveal  the  amount  of  training.  They  were 
as  follows:  (i)  Musical  training  in  public  schools,  (2)  Private 
vocal  lessons  (when,  where,  how  long,  etc.),  (3)  Private  instru- 
mental lessons  (when,  where,  how  long,  etc.).  The  observers  were 
then  equally  grouped  in  two  divisions,  the  first  group  consisting  of 
the  better  ones  in  training  and  expression  and  the  second  of  the 
poorer  ones.  The  mean  threshold  for  each  group  for  the  different 
levels  is  recorded  below: 


Table  IV 

V.d. 
Group  I 
Group  II 

64 
3.8 
3-1 

126       256 
1.2        1.2 
1.5        1-5 

512     1024 

1.8        3-8 
1-6        3.1 

2048 
6.8 
4-9 

We  find,  then,  that  the  group  whose  members  have  had  greatei 
musical  education  and  more  practice  excel  in  capacity  for  discriminat- 


Fig.  8.     Comparison  of  the  musical  and  the  non-musical. 

ing  pitch  only  at  128  and  256  v.d.  But  it  is  in  this  region  that  the 
above  factors  would  have  the  most  influence.  Their  effect  upon  the 
differential  threshold  of  either  extreme  would  be  small  because  these 
tones  are  seldom  used  either  in  singing  or  playing.  There  is,  then, 
some  correlation  between  musical  ability  and  discrimination  of 
pitch  in  the  central  register.  This  is  in  general  agreement  with  the 
conclusions  of  both  Mount  (6)  and  Smith  (15)  who  found  a  fair 
degree  of  correlation  between  musical  expression  of  pitch  and  dis- 


VARIATION  IN  PITCH  DISCRIMINATION  143 

crimination  of  pitch  at  435  v.d.  But  we  cannot  agree  with  Stiicker 
(17)  in  his  assertion  that  musical  observers,  in  general,  show  keener 
discrimination  in  the  upper  limit  than  the  non-musical  ones.  Much 
depends  upon  the  standard  of  classification  for  musical  observers. 
Stiicker  may  have  reference  only  to  observers  of  unusually  fine 
ability  in  music.  For  such,  his  statement  may  be  true,  but  for  ob- 
servers whose  ability  is  not  so  exceptional  it  scarcely  holds. 

The  frequency  and  distribution  of  the  false  judgments. — From 
the  39700  judgments  it  has  been  possible  to  determine  definitely 
not  only  the  frequency  of  the  false  judgments  but  also  the  way 
in  which  they  have  been  distributed  in  the  various  levels.  So  large 
an  amount  of  data  should  show  whether  or  not  there  is  a  preference 
for  one  or  the  other  order,  and  if  so  what  relation  this  preference 
bears  to  sex,  voice-register,  and  pitch. 

In  computing  the  number  of  errors,  the  results  of  sixty-two  indi- 
viduals, thirty-two  women  and  thirty  men,  for  at  least  three  dififerent 
tonal  regions  were  available.  The  nature  of  the  error  in  the  wrong 
judgments  at  64  v.d.  was  not  recorded ;  the  observer  sat  with 
closed  eyes  and  gave  oral  judgments  and  the  experimenter  merely 
recorded  the  number  of  the  errors.  At  the  other  levels,  with  one  or 
two  exceptions,  the  observer  recorded  H  or  L  for  each  pair  of  tones. 
For  128,  256,  512,  1024,  and  2048  v.d.,  then,  the  distribution  of  errors 
could  be  accurately  studied.  Just  one-half  of  the  sixty-two  observers 
had  a  record  for  each  of  these  five  steps,  for  the  other  half  dis- 
criminations were  made  at  from  three  to  four  levels.  Two  different 
computations  were  therefore  made,  the  first  including  the  results  of 
the  entire  number  of  observers  and  the  second,  only  those  which 
are  complete  for  the  five  different  levels.  The  total  of  the  complete 
results  could  thus  be  used  as  a  check  upon  the  total  of  the  incom- 
plete results.  Reference  shall  be  made  to  the  first,  however,  only 
in  so  far  as  it  differs  from  the  second. 

TABLE  V.  Distribution  of  errors 

Section    i 

Computed  from  the  results  of  sixty-two  observers 

A                 B                         C  D  E 

128      8300  23.40  10.78  12.62 

256      8600  25.13  13.31  11.82 

512     loioo  26.03  13-79  12.24 

1024      8300  25.42  13.61  1 1. 81 

2048      4400  25.41  14.00  1 1. 41 

Total    39700  25.09  13.04  12.05 


THOMAS  F.   VANCE 


Section 

2 

Computed 

from 

the  results 

of  thirty  men 

128 

4700 

23.21 

10.34 

12.87 

256 

4800 

25.00 

12.83 

12.17 

5I-' 

6100 

27.46 

13.84 

13.62 

1024 

4500 

24.67 

12.50 

12.17 

2048 

2100 

23.52 

11.61 

1 1. 91 

Total 

22200 

25.11 

' 

12.39 

12.72 

Section  3 

Computed   from  the   results  of  thirty-two   women 

128              3600  23.67  11.36  12.11 

256              3800  25.29  13.92  11.37 

512              4000  23.78  13.48  10.30 

1024              3800  26.32  14.95  11.37 

2048              2300  27.13  16.13  ii.oo 

Total           17500  25.07  13.86  11.21 

Table  V  is  a  record  of  the  errors  computed  from  the  results  of 
the  total  number  of  the  observers.  Column  A  represents  the  vibra- 
tion-rate of  the  fork;  B,  the  total  number  of  judgments;  C,  the  total 
percentage  of  error ;  D,  the  percentage  of  error  when  the  second  tone 
was  lower;  and  E,  the  percentage  of  error  when  the  second  tone 
was  higher.  The  greater  number  of  judgments  in  the  central  regis- 
ter is  due  to  the  fact  that  irregularities  occurring  here  necessitated 
further  experimentation  to  determine  whether  they  were  due  to  sub- 
jective factors  which  were  permanent  or  merely  transient,  or 
possibly  to  objective  factors. 

The  final  average  of  the  percentage  of  right  cases  approaches  to 
within  .09  per  cent,  of  the  ideal  of  75  per  cent.  When  the  different 
levels  are  considered  collectively,  the  false  judgments  amount  to 
13.04  per  cent,  when  the  second  tone  is  lower,  and  to  12.05  per  cent, 
when  the  order  of  succession  is  reversed.  There  seems  then  to  be  a 
slight  though  not  significant  preference  for  the  order  in  which  the 
second  tone  is  higher. 

A  difference  is  observable  in  the  distribution  of  error  at  the  various 
levels.  At  128  v.d.  more  errors  by  1.84  per  cent,  occur  when  the 
second  tone  is  higher,  but  at  the  other  levels  there  is  a  greater  per- 
centage of  error  with  the  opposite  order.  As  shown  in  Table  V  the 
differences  between  Column  D  and  E  increase  gradually  from  256 
to  2048  v.d.  In  the  first  computation,  however,  made  from  the  com- 
plete results  of  a  smaller  number  of  observers,  the  order  of  second 
tone  higher  gives  the  smaller  per  cent,  of  error  at  each  level.  At  128 
v.d.,  the  difference  in  favor  of  this  order  is  only  .48  per  cent.,  but 


VARIATION  IN  PITCH  DISCRIMINATION  145 

at  256  it  amounts  to  2.03  per  cent.,  at  512.  to  3.65  per  cent,  at  1024  to 
2.68  per  cent.,  and  at  2048  v.d.  to  2.46  per  cent.  On  the  average, 
then,  judgments  of  difference  in  pitch  are  more  accurate  when 
the  second  tone  is  higher,  i.e.  given  two  successive  tones  of  the  same 
pitch,  there  is  a  slight  tendency  to  hear  the  second  as  the  higher, 
excepting  at  128  v.d.,  where  fewer  errors  are  made  when  the  reverse 
order  is  followed. 

Difference  of  sex. — When  the  results  are  studied  with  respect  to 
sex  it  is  found  that  the  above  conclusion  would  not  be  valid  for  a 
group  of  individuals  in  which  there  was  a  much  larger  percentage 
of  men  than  women. 

In  the  study  of  differences  of  sex  it  is  found  that  the  women  on  the 
average,  show  a  decided  preference  for  the  order  in  which  the  second 
tone  is  higher  at  every  step  except  at  128  v.d.,  where  the  difference 
seems  to  be  slightly  in  favor  of  the  second  tone  lower.  But  it  is 
at  this  latter  level  that  the  men  show  a  very  strong  preference  for 
the  second  tone  lower,  while  in  the  other  levels  the  difference  in  favor 
of  either  order  is  insignificant.  This  variation  of  sex  affords  addi- 
tional evidence  that  normal  illusions  are  greater  with  women  than 
with  men. 

An  arrangement  of  results  according  to  voice  registers  of  the 
observers  brought  out  nothing  new.  The  difference  seems  to  be 
essentially  between  the  voices  of  men  and  women.  Had  our  ob- 
servers been  highly  specialized  singers,  there  might  have  been  some 
difference  showing  itself  in  the  different  voice  registers. 

TABLE   VI.     Variation  with  sex 

V.d.                   64       128       256       512     1024  2048 

20  women           3.2        1.2        1.4        1.7        3.8  6.6 

16  men                  2.7         l.i         l.o         1.6        2.4  4.8 

The  foregoing  table  and  the  accompanying  figure  show  the  results 
for  the  twenty  women  and  the  sixteen  men  who  had  a  similar 
amount  of  training  in  experimental  procedure.  At  first  sight  there 
seems  to  be  a  decided  difference  between  the  sexes,  inasmuch  as 
the  thresholds  for  men  are  lower  throughout  the  whole  range  than 
those  for  women.  While  there  are  differences  in  favor  of  the  men, 
care  must  be  taken  not  to  attach  too  much  significance  to  them. 
The  differences  at  1024  v.d.,  of  1.4  and  at  2048  v.d.  of  1.8,  seem  to 
be  considerable,  yet  they  are  not  much  greater  than  should  be  ex- 
pected when  the  total  results  are  considered.    At  256  v.d.  the  varia- 


146 


THOMAS  F.  VANCE 


tion  of  .4  appears  high  when  compared  with  the  difference  of  .1  in 
the  octave  just  above  and  just  below.  With  such  noticeable  variation 
in  the  central  region  it  is  not  so  surprising  to  find  much  larger  differ- 
ences at  the  extremes  where  objective  factors  are  not  so  well  con- 
trolled. Smith  (15)  reports  practically  the  same  difference  of  sex 
as  is  shown  in  these  results.  He  finds  that  at  the  ages  of  17  to  20 
and  at  maturity,  the  men  surpass  the  women  by  an  average  of  0.3 
v.d.  at  435  v.d.  It  is  evident  that  the  men's  curve  presents  a  more 
satisfactory  form  than  does  that  of  the  women,  in  that  there  is  not  so 
high  a  variation  between  the  points  of  keenest  discrimination  and  the 


Fig.    9.      The    comparative    curves    of    twenty    women    and    sixteen    men 
together  with  the  composite  of  the  fifty  observers.  (Table  VI). 


extremes.  It  may  be  that  the  cause  of  this  arises  from  a  possible 
inherent  difference  between  the  sexes  in  the  method  of  meeting  new 
situations.  Or  it  may  be  that  the  men  adapt  themselves  more  quickly 
to  experimental  conditions  and  for  this  reason  it  has  been  easier  to 
reach  their  physiological  threshold. 

Stiicker  (17)  contends  that  the  greatest  sensitiveness  to  small 
dift'erences  of  pitch  lies  with  tenors  and  sopranos  in  the  lower  half 
of  their  voice  registers,  but  with  singers  of  bass  and  of  alto  parts, 
as  a  rule,  in  the  upper  half.  In  other  words,  the  differences  is  not  be- 
tween the  voices  of  men  and  the  voices  of  women  but  between  the 
relative  height  and  depth  of  the  voice  register  of  both  sexes.  As 
none  of  my  observers  could  be  classed  as  professional  singers,  the 
results  have  little  to  offer  either  positively  or  negatively,  in  regard  to 
Stiicker's  statement.     Table  VII  indicates  that  only  the  results  of 


VARIATION  IN  PITCH  DISCRIMINATION  147 

the  soprano  singers  can  be  harmonized  with  the  conchision  of 
Stiicker.  The  finest  sensitivity  of  the  tenors  is  in  the  central  part 
of  their  register  and  not  in  the  lower,  as  he  finds  it  to  be ;  the  basses 
made  the  best  record  in  the  lower  part  of  their  register,  rather 
than  in  the  upper ;  the  baritones  have  done  better  in  their  register ; 
and  finally,  the  altos  do  better  in  the  lower  register  and  not  in  the 
upper.  But  these  facts  are  not  necessarily  contradictory  to  Stiicker's, 
inasmuch  as  the  observers  in  this  experiment  represent  only  average 
ability  as  singers.  One  should  have  plotted  the  curves  of  a  relatively 
large  number  of  highly  practiced  singers  before  he  would  be  able  to 
add  a  conclusive  word  in  answer  to  the  problem  which  Stiicker  has 
suggested. 

TABLE  VII.    Average  thresholds  classified  according  to  voice  register 

Soprano  (16)  3.8  1.5  1.6  2.1  4.1  7.1 

Tenor  (  4)  4.1  i-5  i-2  1.2  2.3  4.3 

Baritone  (15)  3-2  14  1.3  2.1  2.4  4.7 

Alto  (  8)  3-5  1-5  1-2  1.3  4-3  6.0 

Bass  (  7)  2.5  I.I  1.3  1.6  2.8  4.3 


SUMMARY 

(i)  For  individuals  selected  because  of  a  slight  superiority  at 
435  v.d.,  the  composite  absolute  curve  of  pitch-discrimination  within 
the  limits  of  64  and  2048  v.d.  shows  the  keenest  discrimination  at 
128  and  256  v.d.  On  either  side  of  this  central  register,  there  is  a 
rise  in  the  curve  which  is  relatively  abrupt  toward  the  lower  limit  but 
much  more  gradual  toward  the  higher  extreme. 

(2)  The  relative  curve  takes  the  form  of  a  continual  decline 
from  the  lower  to  the  higher  limit.  From  64  to  128  v.d.  the  decline 
is  comparatively  steep,  but  from  128  to  2048  v.d.,  it  is  very  gradual, 
approaching  approximately  a  horizontal  line  in  the  upper  half  of 
the  register. 

(3)  Individual  dififerences,  factors  which  lead  to  confusion  and  to 
identification,  and  variation  in  practice  and  in  attention  are  the 
principal  conditions  upon  which  the  form  of  the  curve  depends. 
The  variations  in  the  curves  of  the  different  investigators  are  ex- 
plainable on  the  basis  of  the  varying  degrees  of  influence  of  these 
conditions. 

(4)  Most  of  the  individual  curves  conform  more  or  less  closely 
to  one  of  the  following  types  of  curves;  namely,   (a)   a  curve  in 


148  THOMAS  F.   VANCE 

which  there  is  a  relatively  low  value  at  some  point  in  the  central 
register  and  relatively  high  values  at  the  extremes,  (b)  a  curve  in 
which  the  thresholds  are  fairly  uniform  throughout  the  entire  range, 
and  (c)  one  in  which  the  threshold  for  64  is  considerably  less  than 
for  2048  v.d. 

(5)  There  is  very  little  evidence  of  tonal  gaps.  The  grosser 
irregularities  in  a  few  curves,  which  at  first  seemed  to  indicate  the 
presence  of  a  gap,  disappeared  with  more  extended  observations. 

(6)  A  correlation  between  musical  ability  and  discrimination  of 
pitch  occurs  only  in  the  central  register. 

(7)  The  women  make  more  accurate  judgments  when  the  second 
tone  is  higher;  their  preference  for  this  order  increases  in  direct 
proportion  to  the  pitch,  within  limits,  excepting  at  128  v.d.  where 
the  reverse  order  is  slightly  preferred.  The  men  make  fewer 
mistakes  at  128  v.d.  when  the  second  tone  is  lower,  but  at  the 
other  levels  no  particular  preference  for  either  order  of  succession 
is  observable. 

(8)  The  men  surpass  the  women  in  discrimination  of  pitch  at 
every  level  in  the  register;  this  variation  between  the  sexes  is  the 
greatest  at  the  extremes. 

BIBLIOGRAPHY 

1.  Delezenne.  Recueil  des  travaiix  de  la  Societe  des  Sciences  de 
Lille.     1 826-1 827,  p.  I. 

2.  Faist,  A.  Versuche  iiber  Tonverschmelzung.  Zsch.  f.  Psychol, 
u.  Physiol,  d.  Sinn.,  1897,  15,  102. 

3.  Kiilpe,  O.  Outlines  of  Psychology.  Trans,  by  Titchener,  E.  B. 
New  York;  Macmillan,  1895,  p.  286. 

4.  Luft,  E.  Uber  die  Unterschiedsempfindlichkeit  fur  Tonhohen. 
Phil.  Stud.,  1888,  ^,511. 

5.  Meyer,  M.  Uber  die  Unterschiedsempfindlichkeit  fur  Tonho- 
hen.   Zsch.  f.  Psychol,  u.  Physiol,  d.  Sinn.,  1898,  16,  352. 

6.  Mount,  G.  H.  Correlations  of  Pitch  Discrimination.  (Not  yet 
published). 

7.  Preyer,  W.  Die  Unterschiedsempfindlichkeit  fiir  Tonh5hen. 
Grenaen  der  Tonwahrnehmung ,  Jena,  1876,  p.  24. 

8.  Preyer,  W.  Die  Empfindlichkeit  des  Intervallensinnes.  Ihid.,  38. 

9.  Sauveur,  L.  C.     Memoircs,  p.  395. 

10.  Schaefer,  H.  The  Curve  for  the  Variation  of  Pitch  Discrimina- 
tion within  the  Tonal  Range.  (MS.  in  University  of  Iowa 
Library). 

11.  Schischmanow,  I.  Untersuchungen  uber  die  Empfindlichkeit  des 
Intcrvallsinnes.     Phil.  Stud.,  1889,  5  558. 


VARIATION  IN  PITCH  DISCRIMINATION  149 

12.  Schleiber.  Encyklopddie  d.  ges.  musikal.  Wisscnschaft,  v. 
G.  Schilling,  Stuggart,  1840,  6,  504. 

13.  Seashore,  C.  E.  The  Measurement  of  Pitch  Discrimination: 
A  PreHminary  Report.    Psychol.  Monog.,  1910,  13,  21. 

14.  Seebeci<,  A.    Pogg.  Annalen,  1846,  144,  462. 

15.  Smith,  F.  O.  Effect  of  Training  on  Tonal  Hearing.  (In  this 
volume). 

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hohen  in  Verschiedenen  Tonregionen.  Sitcungsber.  d.  math, 
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42,  392. 

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Macmillan,  1909,  p.  112. 

20.  Weber.    Pogg.  Annalen,  14,  398. 


THE  DURATION  OF  TONES,  THE  TIME  INTERVAL,  THE 

DIRECTION  OF  SOUND,  DARKNESS  AND  QUIET, 

AND  THE  ORDER  OF  STIMULI  IN  PITCH 

DISCRIMINATION 

BY 
DAVID  ALLEN   ANDERSON 

/.  Most  favorable  duratio)i  of  the  tones 
In  this  investigation  to  ascertain  the  relative  favorableness  of 
different  durations  of  tone  in  pitch  discrimination,  the  tones  were 
produced  by  tuning  forks  from  the  "standard  pitch  discrimination 
set"  as  described  by  Professor  Seashore  (i)  reenforced  by  Koenig 
adjustable  resonators  suspended  behind  a  revolving  slit-disc  which 
was  driven  by  a  synchronous  motor  (2,3). 

The  tuning  forks  were  tuned  to  an  accuracy  of  ±  .015  v.d.  They 
were  held  firmly  by  the  fingers  near  the  end  of  the  stem  and  ener- 
gized by  striking  the  middle  of  the  prong  lightly  against  a  sounder 
made  of  %  in.  lead  pipe  covered  with  a  soft  rubber  tubing  and 
resting  on  a  leather  cushion  filled  with  sand.  When  they  had  been  set 
in  motion  the  forks  were  held  directly  in  front  of  the  mouths  of  the 
resonators  during  the  passage  of  the  open  slits  in  the  intervening 
revolving  disc.  Revolving  discs  made  from  cardboard,  in  which 
were  slits  cut  in  appropriate  sectors,  regulated  the  duration  of 
tones  and  the  interval  between  them.  The  disc  proper  prevented  the 
passage  of  the  vibrations  from  the  forks  to  the  resonators  while  the 
slits  admitted  of  their  free  passage.  The  length  of  the  slit  deter- 
mined the  duration  of  the  tone  and  the  size  of  the  sector  between 
governed  the  length  of  the  interval.  When  a  slit  passed  a  fork  the 
resonator  would  take  up  the  vibrations.  The  result  was  a  clear  and 
pure  tone,  clean  cut  at  beginning  and  end.  The  intensity  was  kept 
as  regular  as  possible  without  maintaining  an  identifiable  uniform- 
ity. An  effort  was  made  to  change  the  forks  from  hand  to  hand 
and  to  govern  the  duration  of  time  between  the  energizing  of  the 
forks  and  the  hearing  of  the  tones  in  such  a  way  that  the  observers 
could  get  no  clue  regarding  the  order  in  which  the  tones  were  to  be 
given.  Whether  the  higher  or  lower  tone  was  to  be  given  last  was 
regulated  by  a  key  prepared  beforehand  according  to  chance,  ex- 
cept that  not  more  than  three  consecutive  cases  of  one  kind  were 
allowed. 


»%         '"'-i'^^^M^M 


14  DAY  USE 


